emafit-jfe.f [docs/17c/peakfqSA-jfe-distrib/src] Revision: default Date:
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c****|subroutine emafit
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c REVISED VERSION FROM 2013
c
c this routine fits the pearson type iii distribution to
c a data set using the ema algorithm
c
c this was prepared by tim cohn, us geological survey, to support
c development of an operational version of peakfq (bulletin 17b
c implementation) which would include the expected moments
c algorithm (ema; cohn et al. 1997; 2001)
c
c *** do not modify without author''s consent ***
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c development history
c
c timothy a. cohn 09 nov 2003
c modified 31 dec 2003
c modified 27 mar 2004 (better small skew approx)
c modified 07 dec 2004 (typos in comments corrected)
c modified 07 feb 2007 (major rewrite; reparameterized
c ema in terms of sample moments
c rather than gamma parameters)
c modified 24 may 2007 changed default pqd values (TAC)
c corrected errors (John England)
c modified 05 jun 2007 added gbthrsh0 to subroutine call
c permits user to specify lower bound
c modified 21 jun 2007 corrected error in rGmse treatment wrt
c generalized skew
c modified 13 aug 2007 final low-outlier default procedure
c implemented
c modified 17 aug 2007 final, final LO default procedure
c implemented
c modified 25 sep 2007 final 'argh!' w/update to mseg
c to correct for censored data
c modified 28 feb 2008 computed moments for both B17B
c and EMA at-site MSE(skew)
c modified 18 jun 2008 added constraint to ensure skews
c within reliable range of computation
c modified 02 jul 2008 set default MSE for at-site skew to
c equal B17B MSE when only systematic
c data are present ('ADJE')
c modified 15 sep 2011 set default lskewXmax to .FALSE.
c this determines whether to
c adjust skew so that Qmax is inside
c support of fitted distribution
c (previously set to .TRUE.)
c B17B provides no test or correction
c modified 26 sep 2011 added regional estimate for M
c this is analogous to region S2, G
c modified 24 oct 2011 simplified calls to p3est; results same
c modified 08 feb 2012 added return for var_est in
c modified 10 oct 2012 added redefined computation method for
c mn2m_var using inverse modified
c Cholesky Gaussian Quadrature
c modified 14 feb 2013 added effective record length for skew
c returned in /tac005/...,as_G_ERL
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c NEW VERSION 05 jan 2011 employs
c 1) Multiple Grubbs-Beck Test
c 2) Regional standard deviation
c
c modified 08 apr 2011 fixed MGBT to deal with more than
c 50% zero flows
c
c NEW VERSION 05 Mar 2013 employs
c 1) Inverse Gaussian Quadrature CI
c modified 19 Mar 2014 nu_min increased to 5.d0 from 0.5d0
c
C
C modifications by John England denoted with C JFE
C
C 12-DEC-2014 p3est_ema expand loop for cycling
C 18-MAR-2015 initial notes on pqd block data expansion
C 07-SEP-2017 extended some arrays to 20000
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c n.b. use of ema requires two distinct types of information:
c
c a. "observations," which are described by {ql,qu};
c specifically, the true value of q is assumed to lie
c wihin the interval ql(i) <= q(i) <= qu(i);
c if q(i) is known exactly, then ql(i) = q(i) = qu(i);
c
c {ql,qu} are required by ema to fit p3 distn to data
c
c b. "censoring pattern," which is described by {tl,tu}
c {tl,tu} define the interval on which data get observed:
c if q is not inside {tl,tu}, q is either left or right
c censored.
c
c examples:
c {-inf,+inf} => systematic data (exact value of q
c would be measured)
c {t, +inf} => historical data
c q>=t would be known exactly;
c q<t would be reported as censored ("less-than")
c
c {tl,tu} are required by ema to estimate confidence
c intervals; they are not required for frequency
c curve determination
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c n i*4 number of observations (censored, uncensored, or
c other)
c ql(n) r*8 vector of lower bounds on (log) floods
c qu(n) r*8 vector of upper bounds on (log) floods
c NOTE: Zero flows enter as lmissing=-80.d0
c tl(n) r*8 vector of lower bounds on (log) flood threshold
c tu(n) r*8 vector of upper bounds on (log) flood threshold
c dtype(n) c*4 vector describing input data
c dtype(i) = "Syst" => systematic data
c dtype(i) = "Hist" => historic data
c dtype(i) = "Othr" => other
c reg_SD r*8 regional standard deviation
c reg_SD_mse r*8 mean square error of generalized standard deviation
c notes:
c 1) reg_SD_mse = 0 ("GENERALIZED STD DEV, NO ERROR")
c use fixed parms(*) = reg_SD w/ mse = 0.0
c 2) -999 < reg_SD_mse< 0 ("AT-SITE STD DEV")
c use at-site estimated standard deviation
c 3) 0 < reg_SD_mse < 1.d10 ("WEIGHTED STD. DEV.")
c use sd = weighted average of at-site and
c regional standard deviation
c r_G r*8 regional skew
c r_G_mse r*8 mean square error of regional skew
c this variable encodes four distinct cases:
c 1) r_G_mse = 0 ("GENERALIZED SKEW, NO ERROR")
c use fixed g = r_G w/ mse = 0.0
c 2) -98 < r_G_mse < 0 ("GENERALIZED SKEW, MSE > 0")
c use fixed g = w/ mse = -r_G_mse
c 3) 0 < r_G_mse < 1.d10 ("WEIGHTED SKEW")
c use g = weighted average of at-site and
c regional skew (b17b recommendation)
c 4) 1.d10 < r_G_mse ("STATION SKEW")
c use g = at-site skew
c gbtype c*4 type of Grubbs-Beck test
c = "GBT" => standard GB test
c = "MGBT" => Multiple GB test
c gbthrsh0 r*8 critical value for Grubbs-Beck test
c N.B. gbthrsh0 codes for 3 cases
c 1. gbthrsh0 <= -6 ==> Compute GB critical value
c 2. gbthrsh0 > -6 ==> gbthrsh0 as crit. val.
c 3. gbthrsh0 (small, e.g. -5.9) no low out. test
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c output variables:
c ------------------------------------------------------------------------
C JFE number of quantiles expanded fromn 32 to 41
C JFE use the blkdata to restrict or expand further
c
c cmoms(3,3) r*8 first 3 central moments
c (,1) using regional info and at-site data
c (,2) using just at-site data
c (,3) using B17B formula for at-site MSE(G)
c mc = {mean, variance, coeff. skew}
c JFE pq(41 was 32) r*8 quantiles estimated
c --pq=0.99 corresponds to "100-year flood"
C JFE nq varies and expanded to 41 from 32
c nq i*4 number of quantiles estimated (41) (TAC = 32)
c yp(41) r*8 estimated pq-th quantile of fitted p3 distribution
c ci_low(41) r*8 left end of 95% confidence interval for pq-th
c quantile
c ci_high(41)r*8 right end of 95% confidence interval for pq-th
c quantile
cprh (09/2009)
c var_est(*) r*8 variance of estimate for each quantile
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c parameters set in common block data/emablk/ (can be reset if desired)
c ------------------------------------------------------------------------
c /tacg04/at_site_std c*4 formula employed for computing mse of
c estimated at-site skew
c 'B17B' => Bulletin 17B MSE formula
c 'EMA' => First-order EMA MSE
c 'ADJE' => Adjusted first-order (Default)
c
c /MGB001/Alpha(3) r*8 alpha level for MGBT check for low outliers
c Default value is 0.01 [corr. 1% test]
c Step 1. Outward sweep from median (always done).
c alpha level of test = Alphaout Alpha(1)
c number of outliers = J1
c
c Step 2. Inward sweep from largest low outlier identified in Step 1.
c alpha level of test = Alphain Alpha(2)
c number of outliers = J2
c
c Step 3. Inward sweep from smallest observation
c alpha level of test = Alphazeroin Alpha(3)
c number of outliers = J3
c
c
c /tac002/sk141 r*8 minimum value of skew
c Default value is -1.41
c
c /tac002/bcf r*8 bias correction factor to use for S2, G
c 1997 => Cohn [1997] factors (Default)
c 2004 => Griffis et al. [2004] factors
c 0 => None
c
c /tac002/lskewXmax r*8 do you want to test fitted support to
c include Qmax?
c Default value is .FALSE.
c
c /tacR01/VarS2opt c*4 formula employed for computing weighting of
c at-site and regional info for computing S2
c (the problem: MSE of \hat{S^2} proportional
c to \sigma^4; we have two estimates of \sigma
c at-site and regional. What should weight
c reflect?)
c 'DF' => inversely to degrees of freedom
c df = 2*(S^4)/MSE[S^2] (DEFAULT)
c 'S2' => inversely to MSE[S^2_{at-site}]
c and MSE[S^2_{regional}]
c 'S1' => inversely to MSE[S_{at-site}]
c and MSE[S_{reg.}] (NOT AVAIL.)
c
c /tacci1/eps r*8 nominal conf. int. coverage (90% def.)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine emafit(n,ql,qu,tl,tu,dtype,
1 reg_SD,reg_SD_mse,r_G,r_G_mse,gbtype,gbthrsh0,
1 cmoms,pq,nq,yp,ci_low,ci_high,var_est)
implicit none
integer
1 i,n,nq,nqd ! input variables
double precision
1 ql(*),qu(*),tl(*),tu(*),reg_SD,reg_SD_mse,r_G,r_G_mse, ! input variables
2 cmoms(3,3),pq(*),yp(*),ci_low(*),ci_high(*),var_est(*),! output vars
3 pqd,eps,gbthrsh0,
4 r_M,r_M_mse,r_S2,r_S2_mse
character*4
1 dtype(*),gbtype
common /tacpq1/pqd(100),nqd
common /tacci1/eps
c
c set regional information for mean equal to zero
c
r_M = 0.d0
r_M_mse = -99.d0 ! ignore regional info on M
c
c calculate stats for variances (S^2) from standard deviations input
c
r_S2 = reg_SD**2
r_S2_mse = 4.d0 * r_S2 * reg_SD_mse ! first order approximation
nq = nqd
do 10 i=1,nq
pq(i) = pqd(i)
10 continue
call emafitb(n,ql,qu,tl,tu,dtype,
1 r_M,r_M_mse,r_S2,r_S2_mse,r_G,r_G_mse,
1 eps,gbtype,gbthrsh0,pq,nq,
1 cmoms,yp,ci_low,ci_high,var_est)
c
c correction to adjust for small sample sizes (see tac notes 17 feb 2007)
c
do 20 i=(nq-1)/2,1,-1
ci_low(i) = min(ci_low(i),ci_low(i+1))
ci_high(i) = min(ci_high(i),ci_high(i+1))
20 continue
do 30 i=(nq+3)/2,nq
ci_low(i) = max(ci_low(i),ci_low(i-1))
ci_high(i) = max(ci_high(i),ci_high(i-1))
30 continue
return
end
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c****|subroutine emafitpr
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c REVISED VERSION FROM 2011
c
c this routine fits the pearson type iii distribution to
c a data set using the ema algorithm.
c it includes the ability to employ regional information on 3 parameters
c otherwise it works the same as emafit
c
c so far this feature is not adequately documented
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c development history
c
c timothy a. cohn 26 sep 2011 added regional estimate for M
c this is analogous to region S2, G
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c n i*4 number of observations (censored, uncensored, or
c other)
c ql(n) r*8 vector of lower bounds on (log) floods
c qu(n) r*8 vector of upper bounds on (log) floods
c NOTE: Zero flows enter as lmissing=-80.d0
c tl(n) r*8 vector of lower bounds on (log) flood threshold
c tu(n) r*8 vector of upper bounds on (log) flood threshold
c dtype(n) c*4 vector describing input data
c dtype(i) = "Syst" => systematic data
c dtype(i) = "Hist" => historic data
c dtype(i) = "Othr" => other
c reg_M r*8 regional mean (M)
c reg_M_mse r*8 mean square error of generalized mean
c notes:
c 1) reg_M_mse = 0 ("GENERALIZED MEAN, NO ERROR")
c use fixed parms(*) = reg_M w/ mse = 0.0
c 2) -999 < reg_M_mse< 0 ("AT-SITE MEAN")
c use at-site estimated mean
c 3) 0 < reg_M_mse < 1.d10 ("WEIGHTED MEAN")
c use M = weighted average of at-site and
c regional mean
c reg_SD r*8 regional standard deviation
c reg_SD_mse r*8 mean square error of generalized standard deviation
c notes:
c 1) reg_SD_mse = 0 ("GENERALIZED STD DEV, NO ERROR")
c use fixed parms(*) = reg_SD w/ mse = 0.0
c 2) -999 < reg_SD_mse< 0 ("AT-SITE STD DEV")
c use at-site estimated standard deviation
c 3) 0 < reg_SD_mse < 1.d10 ("WEIGHTED STD. DEV.")
c use sd = weighted average of at-site and
c regional standard deviation
c r_G r*8 regional skew
c r_G_mse r*8 mean square error of regional skew
c this variable encodes four distinct cases:
c 1) r_G_mse = 0 ("GENERALIZED SKEW, NO ERROR")
c use fixed g = r_G w/ mse = 0.0
c 2) -98 < r_G_mse < 0 ("GENERALIZED SKEW, MSE > 0")
c use fixed g = w/ mse = -r_G_mse
c 3) 0 < r_G_mse < 1.d10 ("WEIGHTED SKEW")
c use g = weighted average of at-site and
c regional skew (b17b recommendation)
c 4) 1.d10 < r_G_mse ("STATION SKEW")
c use g = at-site skew
c gbtype c*4 type of Grubbs-Beck test
c = "GBT" => standard GB test
c = "MGBT" => Multiple GB test
c gbthrsh0 r*8 critical value for Grubbs-Beck test
c N.B. gbthrsh0 codes for 3 cases
c 1. gbthrsh0 <= -6 ==> Compute GB critical value
c 2. gbthrsh0 > -6 ==> gbthrsh0 as crit. val.
c 3. gbthrsh0 (small, e.g. -5.9) no low out. test
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c output variables:
c ------------------------------------------------------------------------
c
c cmoms(3,3) r*8 first 3 central moments
c (,1) using regional info and at-site data
c (,2) using just at-site data
c (,3) using B17B formula for at-site MSE(G)
c mc = {mean, variance, coeff. skew}
c pq(32) r*8 quantiles estimated
c --pq=0.99 corresponds to "100-year flood"
c nq i*4 number of quantiles estimated (32)
c yp(32) r*8 estimated pq-th quantile of fitted p3 distribution
c ci_low(32) r*8 left end of 95% confidence interval for pq-th
c quantile
c ci_high(32)r*8 right end of 95% confidence interval for pq-th
c quantile
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine emafitpr(n,ql,qu,tl,tu,dtype,
1 reg_M,reg_M_mse,reg_SD,reg_SD_mse,r_G,r_G_mse,
2 gbtype,gbthrsh0,
2 cmoms,pq,nq,yp,ci_low,ci_high,var_est)
implicit none
integer
1 i,n,nq,nqd ! input variables
double precision
1 ql(*),qu(*),tl(*),tu(*),reg_SD,reg_SD_mse,r_G,r_G_mse, ! input vars
2 cmoms(3,3),pq(*),yp(*),ci_low(*),ci_high(*),var_est(*),! output vars
3 pqd,eps,gbthrsh0,
4 reg_M,reg_M_mse,r_M,r_M_mse,r_S2,r_S2_mse
character*4
1 dtype(*),gbtype
ctac data eps/0.90d0/,nqd/32/
common /tacpq1/pqd(100),nqd
common /tacci1/eps
c 1. bring in regional information for M, S, and g
c 1a. set regional information for mean
r_M_mse = reg_M_mse
if(r_M_mse .le. 0.d0) then
r_M = 0.d0
r_M_mse = -99.d0
else
r_M = reg_M
r_M_mse = reg_M_mse
endif
c 1b. set regional information for variance
c
c calculate stats for variances (S^2) from standard deviations input
c N.B. This is an approximation. The results would be slightly different
c if regionalization were done on S^2 or if estimation weighting
c were done on S. However, this is more convenient given the
c parametrization based on (M, S2, G) rather than (M, S, G)
c
r_S2 = reg_SD**2
r_S2_mse = 4.d0 * r_S2 * reg_SD_mse ! first order approximation
c 1c. regional information for skew must be supplied by user as argument
nq = nqd
do 10 i=1,nq
pq(i) = pqd(i)
10 continue
call emafitb(n,ql,qu,tl,tu,dtype,
1 r_M,r_M_mse,r_S2,r_S2_mse,r_G,r_G_mse,
1 eps,gbtype,gbthrsh0,pq,nq,
1 cmoms,yp,ci_low,ci_high,var_est)
c
c correction to adjust for small sample sizes (see tac notes 17 feb 2007)
c
do 20 i=(nq-1)/2,1,-1
ci_low(i) = min(ci_low(i),ci_low(i+1))
ci_high(i) = min(ci_high(i),ci_high(i+1))
20 continue
do 30 i=(nq+3)/2,nq
ci_low(i) = max(ci_low(i),ci_low(i-1))
ci_high(i) = max(ci_high(i),ci_high(i-1))
30 continue
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine emafitb
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c the main subroutine
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c n i*4 number of observations (censored, uncensored, or
c other)
c ql(n) r*8 vector of lower bounds on (log) floods
c qu(n) r*8 vector of upper bounds on (log) floods
c tl(n) r*8 vector of lower bounds on (log) flood threshold
c tu(n) r*8 vector of upper bounds on (log) flood threshold
c dtype(n) c*4 vector describing input data
c dtype(i) = "Syst" => systematic data
c dtype(i) = "Hist" => historic data
c dtype(i) = "Othr" => other
c r_M r*8 regional mean
c r_M_mse r*8 mean square error of regional mean
c 1) r_M_mse = 0 ("GENERALIZED MEAN, NO ERROR")
c use fixed M = r_M w/ mse = 0.0
c 2) -999 < r_M_mse < 0 ("AT-SITE MEAN")
c use at-site estimated mean (M)
c 3) 0 < r_M_mse < 1.d10 ("WEIGHTED MEAN")
c use M = weighted average of at-site and
c regional variance
c r_S2 r*8 regional variance (std.dev^2)
c N.B. Needed because var. of regional S2 scales
c with (E[S2])^2; weights for S2 is based
c on degrees of freedom in Chi-square dstn
c corresponding to each estimator where
c df = (1/2) S2^2/\hat{Var[S^2]}
c r_S2_mse r*8 mean square error of regional variance
c 1) r_S2_mse = 0 ("GENERALIZED S2, NO ERROR")
c use fixed sd = reg_SD w/ mse = 0.0
c 2) -999 < r_S2_mse < 0 ("AT-SITE VARIANCE")
c use at-site estimated variance (S^2)
c 3) 0 < r_S2_mse < 1.d10 ("WEIGHTED VARIANCE")
c use S2 = weighted average of at-site and
c regional variance
c r_G r*8 regional skew
c r_G_mse r*8 mean square error of regional skew
c this variable encodes four distinct cases:
c 1) r_G_mse = 0 ("GENERALIZED SKEW, NO ERROR")
c use fixed g = r_G w/ mse = 0.0
c 2) -98 < r_G_mse < 0 ("GENERALIZED SKEW, MSE > 0")
c use fixed g = r_G w/ mse = -r_G_mse
c 3) 0 < r_G_mse < 1.d10 ("WEIGHTED SKEW")
c use g = weighted average of at-site and
c regional skew (b17b recommendation)
c 4) 1.d10 < r_G_mse ("STATION SKEW")
c use g = at-site skew
c pq r*8 quantile to be estimated
c --pq=0.99 corresponds to "100-year flood"
c nq i*4 number of quantiles estimated (32)
c eps r*8 vector of ci coverages (usually just 0.90)
c gbthrsh0 r*8 critical value for Grubbs-Beck test
c (values < -6 result in computed low outlier
c test criterion)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c output variables:
c ------------------------------------------------------------------------
c
c cmoms(3,3) r*8 first 3 central moments
c mc = {mean, variance, coeff. skew}
c yp r*8 estimated pq-th quantile of fitted p3 distribution
c ci_low r*8 left end of 90% confidence interval for pq-th
c quantile
c ci_high r*8 right end of 90% confidence interval for pq-th
c quantile
cprh (09/2009)
c var_est r*8 variance of estimate for each quantile
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine emafitb(n,ql_in,qu_in,tl_in,tu_in,dtype_in,
1 r_M,r_M_mse,r_S2,r_S2_mse,r_G,r_G_mse,
1 eps,gbtype_in,gbthrsh0,pq,nq,
2 cmoms,yp,ci_low,ci_high,var_est)
implicit none
integer
1 ntmax,nn,nx
parameter (ntmax=100,nn=100,nx=25000)
integer
1 n,i,nt,ns,nlow,nzero,nGBiter,nlow_V,it_max,nq
double precision
1 ql_in(*),qu_in(*),tl_in(*),tu_in(*),
1 r_M,r_M_mse,r_S2,r_S2_mse,r_G,r_G_mse,pq(*), ! input
2 cmoms(3,3),yp(nn),ci_low(nn),ci_high(nn),var_est(nn), ! output
3 yp1(nn),yp2(nn),ci_low1(nn),ci_low2(nn),ci_high1(nn),
4 ci_high2(nn),skewmin,qP3,parms(3),
5 ql,qu,tl,tu,qs,
6 cv_yp_syp(2,2,nn),eps,tl2(ntmax),tu2(ntmax),nobs(ntmax),
7 skew,wt,as_M_mse,as_S2_mse,as_G_mse,as_G_mse_Syst,as_G_ERL,
8 eff_n,gbthrsh0,gbcrit,gbthresh,gbcrit_V,gbthresh_V,pvaluew
parameter (skewmin=0.06324555)
double precision
1 mseg_all,mse_ema
character*4
1 at_site_option,at_site_default,at_site_std,gbtype,gbtype_in,
2 dtype,dtype_in(*),VarS2opt
logical cirun
C JFE
C common /tacg01/gbcrit,gbthresh,pvaluew(10000),qs(10000),
common /tacg01/gbcrit,gbthresh,pvaluew(20000),qs(20000),
1 ns,nlow,nzero,gbtype
common /tacg02/ql(nx),qu(nx),tl(nx),tu(nx),dtype(nx)
common /tacg03/gbcrit_V(10),gbthresh_V(10),nlow_V(10),nGBiter
common /tacg04/at_site_option,at_site_default,at_site_std
common /tacdgb/cirun
common /tac005/as_M_mse,as_S2_mse,as_G_mse,as_G_mse_Syst,as_G_ERL
common /tacR01/VarS2opt
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c 1. check for low outliers
c a) Identify/recode LOs based on at-site systematic + historical data
c b) Iterate search for LOs using at-site systematic + historical data
c combined with regional skew information
c
do 12 i=1,n
ql(i) = ql_in(i)
qu(i) = qu_in(i)
tl(i) = tl_in(i)
tu(i) = tu_in(i)
12 continue
gbtype = gbtype_in
c loop up to 10 times to see if any new LOs uncovered
if(gbtype .eq. 'GBit') then
it_max = 10
else
it_max = 1
endif
do 15 i=1,it_max
call gbtest(n,ql,qu,tl,tu,dtype_in,gbthrsh0,
1 ql,qu,tl,tu)
gbcrit_V(i) = gbcrit
gbthresh_V(i) = gbthresh
nlow_V(i) = nlow
if(nlow .eq. 0) goto 17 ! any new low outliers?
15 continue
if(gbtype .eq. 'GBit') then
write(*,*) ' Low outlier issues (emafit): nlow = ', nlow,i
write(*,*) ' User may want to specify threshold'
stop ! Should never get here; something is wrong
endif
17 continue
nGBiter = i ! added on JRS recomendation
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c If we have censoring due to low outliers using new MGBT, the MSE of
c at-site skew will tend to stay constant or decline because skew
c will be driven toward zero.
c Thus first-order approximation based on fixed censoring, which would
c suggest increased MSE, is incorrect.
c As a temporary fix, if MGBT is used and low outliers are detected,
c the B17B formula will be used to estimate the MSE of the skew.
c
if(gbtype .eq. "MGBT" .and. nlow .gt. 0) then
at_site_std = "B17B"
else
at_site_std = "ADJE" ! correction due to PRH 12/16/2013
endif
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c 2. organize data for computing ci and set up the tl and tu vectors
c
call compress2(n,tl,tu,nt,nobs,tl2,tu2)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c 3. begin by fitting the p3 distn to the at-site and regional data
c
c n.b. three calls are necessary:
c 1. compute at-site moments without employing regional skew;
c this is used to compute the MSE(G) and moments for
c the case of only at-site data employing the B17B
c formula for MSE(G) [this is a very poor approximation
c when historical info or left-tail censoring is present].
c However, the moments are needed to compute at-site MSEs
c for call 2.
c 2. EMA/B17B computation using regional skew information
c with B17B MSE(G) formula (B17B eqn 6; p. 13)
c 3. final computation using regional skew information
c with EMA MSE(G)
c
c 1) Get at-site skews
call p3est_ema(n,ql,qu,
1 1.d0, 1.d0, 1.d0, ! set all at-site MSEs to 1
2 r_M, r_S2, r_G,
3 -99.d0, -99.d0, -99.d0, ! set all regional MSEs to Infinity
4 cmoms(1,2)) ! return moments (only skew is needed)
c 2) EMA computation using weighted regional information/B17B MSEs
at_site_option = "B17B"
as_M_mse = mse_ema(nt,nobs,tl2,tu2,cmoms(1,2),1) ! compute true a-s
as_S2_mse = mse_ema(nt,nobs,tl2,tu2,cmoms(1,2),2) ! MSEs based on at-
as_G_mse = mseg_all(nt,nobs,tl2,tu2,cmoms(1,2)) ! site skew cmoms(1,3)
c
eff_n = dble(max(ns,10)) ! use a reasonable sample size if ns=0
as_G_mse_Syst = mseg_all(1,eff_n,-99.d0,99.d0,cmoms(1,2)) ! ERL Computation
as_G_ERL = dble(eff_n)*(as_G_mse_Syst/as_G_mse)
call p3est_ema(n,ql,qu,
1 as_M_mse,as_S2_mse,as_G_mse,
2 r_M, r_S2, r_G,
3 r_M_mse, r_S2_mse, r_G_mse,
4 cmoms(1,3))
c 3) final computation using weighted regional info
if(at_site_std .ne. 'B17B') then
at_site_option = at_site_std
as_M_mse = mse_ema(nt,nobs,tl2,tu2,cmoms(1,2),1) ! compute true a-s
as_S2_mse = mse_ema(nt,nobs,tl2,tu2,cmoms(1,2),2) ! MSEs based on at-
as_G_mse = mseg_all(nt,nobs,tl2,tu2,cmoms(1,2)) ! site skew cmoms(1,3)
as_G_mse_Syst = mseg_all(1,eff_n,-99.d0,99.d0,cmoms(1,2)) ! ERL
as_G_ERL = dble(eff_n)*(as_G_mse_Syst/as_G_mse)
call p3est_ema(n,ql,qu,
1 as_M_mse,as_S2_mse,as_G_mse, ! use at-site MSEs
2 r_M, r_S2, r_G, ! and weighted regional info
3 r_M_mse, r_S2_mse, r_G_mse,
4 cmoms(1,1)) ! these are the EMA results
else
cmoms(1,1) = cmoms(1,3)
cmoms(2,1) = cmoms(2,3)
cmoms(3,1) = cmoms(3,3)
endif
if(.not. cirun) return
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c 4. compute confidence intervals
c
if( abs(cmoms(3,1)) .gt. skewmin) then
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c 4.1 for skews far from zero
c
call var_emab(nt,nobs,tl2,tu2,cmoms,pq,nq,eps,
1 r_s2, r_m_mse, r_s2_mse, r_g_mse,
3 yp,cv_yp_syp,ci_low,ci_high)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c 4.2 for skews close to zero; preserves mean and variance
c
else ! compute a weighted sum/interpolate values
skew = cmoms(3,1)
cmoms(3,1) = -skewmin
call m2p(cmoms,parms)
call var_emab(nt,nobs,tl2,tu2,cmoms,pq,nq,eps,
1 r_s2,
2 r_m_mse, r_s2_mse, r_g_mse,
3 yp1,cv_yp_syp,ci_low1,ci_high1)
cmoms(3,1) = skewmin
call m2p(cmoms,parms)
call var_emab(nt,nobs,tl2,tu2,cmoms,pq,nq,eps,
1 r_s2,
2 r_m_mse, r_s2_mse, r_g_mse,
3 yp2,cv_yp_syp,ci_low2,ci_high2)
wt = (skew+skewmin)/(2.d0 * skewmin) ! weight to attach to positive skew
cmoms(3,1) = skew
c compute weighted average of results (assume approx. linear)
do 20 i=1,nq
yp(i) = qP3(pq(i),cmoms)
ci_low(i) = (1.d0-wt) * ci_low1(i) + wt * ci_low2(i)
ci_high(i) = (1.d0-wt) * ci_high1(i) + wt * ci_high2(i)
20 continue
endif
c return estimate of log-quantile variance for each quantile
do 30 i=1,nq
var_est(i) = cv_yp_syp(1,1,i)
30 continue
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine gbtest
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c grubbs-beck test (now includes tests for multiple low outliers)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c development history
c
c timothy a. cohn 07 feb 2007
c modified .. ... 2011 New MGBT procedure added
c modified .. ... 2012 New JLaM/JRS MGBT procedure added
c modified 13 feb 2013 ns put into common block
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c n.b. routine takes input data, uses gb test on systematic data to identify
c low outliers, then recodes low outliers as censored values
c where threshold is set at first above-gb-critical value
c observation.
c routine is not iterative
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c n i*4 number of observations (only systematic data)
c ql_in(n) r*8 vector of lower bounds on (log) floods
c qu_in(n) r*8 vector of upper bounds on (log) floods
c tl_in(n) r*8 vector of lower bounds on (log) flood threshold
c tu_in(n) r*8 vector of upper bounds on (log) flood threshold
c gbthrsh0 r*8 critical value for Grubbs-Beck test
c (0 or negative values => estimate threshold)
c (small value (1e-10) => no low outlier test)
c as_G_mse r*8 mse of at-site skew estimate
c r_G r*8 regional skew
c r_G_mse r*8 mean square error of regional skew
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c output variables:
c ------------------------------------------------------------------------
c
c ql(n) r*8 vector of lower bounds on (log) floods
c qu(n) r*8 vector of upper bounds on (log) floods
c tl(n) r*8 vector of lower bounds on (log) flood threshold
c tu(n) r*8 vector of upper bounds on (log) flood threshold
c
c n.b. routine also returns info (used by PeakfqSA) on number of
c systematic observations, low outliers, etc. through common block
c
c common /tacg01/gbcrit,gbthresh,pvaluew(10000),qs(10000),
c ns,nlow,nzero,gbtype
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine gbtest(n,ql_in,qu_in,tl_in,tu_in,dtype,gbthrsh0,
1 ql,qu,tl,tu)
implicit none
integer
1 n,ns,i,nlow,klow,
2 nzero
integer p_nq
parameter (p_nq=20000)
double precision
1 ql_in(*),qu_in(*),tl_in(*),tu_in(*),
2 ql(*),qu(*),tl(*),tu(*),gbcrit,gbthresh,gbthrsh0,qs,
3 x(p_nq),xm,s,t,cmoms(3),gbtmin,pvaluew,
5 lmissing,qmin
integer MGBTP
character*4
1 gbtype,dtype(*)
C JFE common /tacg01/gbcrit,gbthresh,pvaluew(10000),qs(10000),
common /tacg01/gbcrit,gbthresh,pvaluew(20000),qs(20000),
1 ns,nlow,nzero,gbtype
data gbtmin/-6.d0/,lmissing/-80.d0/
! allows very small positive log(q) values
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c compute number of systematic flows (ns) and count zero flows (nzero)
c note that zero flows are automatically treated as low outliers in MGBT
ns = 0
nzero = 0
qmin = 99.d99 ! identify the smallest 'Syst'
do 10 i=1,n
if(ql_in(i) .eq. qu_in(i) .and. dtype(i) .eq. 'Syst') then ! N.B. Criterion
ns = ns + 1
x(ns) = ql_in(i)
qmin = min(qmin,x(ns))
qs(ns)= 10**x(ns)
if(qu_in(i) .le. lmissing) nzero = nzero + 1
endif
10 continue
c===
c
c determine if there is a 'less-than' value known to be smaller than smallest
c point value; these are also treated as systematic observations
if(qmin .lt. 99.d99) then
do 15 i=1,n
if( (ql_in(i) .ne. qu_in(i)) .and.
1 (dtype(i) .eq. 'Syst') .and.
2 (qu_in(i) .le. qmin) ) THEN
ns = ns + 1
x(ns) = qu_in(i)
qs(ns)= 10**x(ns)
endif
15 continue
endif
c
c===
c no low outlier test
if(gbtype .eq. "NONE") then
gbthresh = -99.d0
gbcrit = gbthresh
goto 25
endif
c specified low outlier threshold?
if(gbtype .eq. "FIXE") then
gbthresh = gbthrsh0
gbcrit = gbthrsh0
goto 25
endif
call dsvrgn(ns,x,x)
call dsvrgn(ns,qs,qs)
if( (ns-nzero) .le. 5) then ! not enough data>0 to apply low-outlier test
write(*,*) 'inadequate data for grubbs-beck test',ns-nzero
write(*,*) 'all zeroes recoded as smaller than: ',qs(nzero+1)
write(*,*) 'this is the smallest non-zero systematic obs.'
gbcrit = x(nzero+1)
gbthresh = x(nzero+1)
goto 25
endif
c
c Limit of use of MGBT Test; substitute GB when over half zeros
c
if( (gbtype .eq. 'MGBT') .and. (nzero .ge. ns/2) ) then
gbtype = 'GBT'
write(*,*) 'too many zeros for MGBT test (ns, nzero) ',ns,nzero
write(*,*) 'traditional Grubbs-Beck (GB) used instead'
endif
c
c Traditional Grubbs-Beck Test (error noted on 3/24/2013; n where ns needed)
c
if(gbtype .eq. 'GBT') then ! B17B Grubbs-Beck test for 1 outlier
call p3est_ema(ns-nzero,x(nzero+1),x(nzero+1), ! changed to ns from n
1 1.d0, 1.d0, 1.d0, ! At-site MSEs
2 0.d0, 1.d0, 0.d0, ! Regional parameters (dumb)
3 -99.d0,-99.d0,-99.d0, ! use no regional info
4 cmoms) ! get moms
xm = cmoms(1)
s = sqrt(cmoms(2))
t = -0.9043+3.345*sqrt(log10(dble(ns-nzero))) ! N.B. ns, not n
1 -0.4046*log10(dble(ns-nzero)) ! Lu formula [JRS]
gbcrit = xm - s*t
gbthresh= 1.d10 ! starting value to find gbthresh
do 20 i=1,ns
if(x(i) .ge. gbcrit) then
gbthresh = min(x(i),gbthresh)
endif
20 continue
c
c Multiple Grubbs-Beck Test
c
else if(gbtype .eq. "MGBT") then ! Multiple Grubbs-Beck (Cohn, 2011)
klow = MGBTP(qs,ns,pvaluew)
if(klow .gt. 0) then
gbcrit = x(klow+1)
gbthresh = gbcrit
else
if(nzero .gt. 0) then ! zero flows are low outliers
klow = nzero
gbcrit = x(klow+1)/2.d0 ! smallest obs > 0 divided by 2...why not?
gbthresh = x(klow+1)
else
gbcrit = -99.d0 ! no low outlier issues
gbthresh = gbcrit
endif
endif
endif
c fill in various arrays and compute nlow
25 continue
nlow = 0
do 30 i=1,n
if(qu_in(i) .lt. gbcrit) then ! note:
nlow = nlow+1
qu(i) = gbthresh
ql(i) = gbtmin
else
ql(i) = ql_in(i)
qu(i) = qu_in(i)
endif
tl(i) = max(tl_in(i),gbcrit) ! change made 13 aug 07 (TAC)
! note: recode to smallest X>Crit_GB
tu(i) = tu_in(i)
30 continue
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine p3est_ema
c****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c fits pearson type iii distribution to censored data using
c an em algorithm and method of moments estimators
c
c fits binomial-censored data
c
c author....tim cohn
c date......february 9, 1994
c
c modified 2/8/1995 tac
c modified 2/22/1995 tac
c modified 12/16/1996 tac fixed bias-correction factors
c and added second convergence criterion
c modified 11/17/1998 tac conv crit. added
c modified 03/13/1999 tac removed bias correction factors
c modified 09/28/2011 tac changed call arguments; added regional M, S2
c
c****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c modified 10/31/98 tac; added regional skewness/fixed skewness
c capability; note that call now has two
c additional arguments:
c r_G is the regional skew
c reg_wgt is the relative weight (0-1) to
c assign regional vs at-site skew
c
c****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c n i*4 number of observations (censored, uncensored, or
c other)
c ql(n) r*8 vector of lower bounds on (log) floods
c qu(n) r*8 vector of upper bounds on (log) floods
c as_M_mse r*8 mean square error of at-site mean (M)
c this is calculated by mse_ema
c as_S2_mse r*8 mean square error of at-site variance (S2)
c this is calculated by mse_ema
c as_G_mse r*8 mean square error of at-site skew (G)
c this is calculated by mseg_all
c r_M r*8 regional mean (M)
c r_S2 r*8 regional variance (std.dev^2) (S2)
c r_G r*8 regional skew (G)
c r_M_mse r*8 mean square error of regional mean
c r_S2_mse r*8 mean square error of regional variance
c r_G_mse r*8 mean square error of regional skew
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c output variable:
c ------------------------------------------------------------------------
c
c cmoms(3) r*8 first 3 central moments
c mc = {mean, variance, coeff. skew}
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c note: ql(i) is the lower bound for the i-th observation
c qu(i) is the upper bound
c if( qu == ql) then we have an ordinary observation at qu
c
c
subroutine p3est_ema(n,ql,qu,
1 as_M_mse,as_S2_mse,as_G_mse, ! use at-site MSEs
2 r_M, r_S2, r_G, ! and weighted regional info
3 r_M_mse, r_S2_mse, r_G_mse,
4 moms_out)
implicit none
integer
1 n,nsize,i,j,k
character*4 VarS2opt
common /tacR01/VarS2opt
common /reg001/rM,rMmse,rS2,rS2mse,rG,rGmse
parameter (nsize=20001)
double precision
1 ql(*),qu(*),as_M_mse,as_S2_mse,as_G_mse,
1 r_M, r_S2, r_G,
3 r_M_mse, r_S2_mse, r_G_mse,
4 moms_out(3),
2 moms(3,nsize),d11(nsize),dist_p3,tol,
3 rM,rMmse,rS2,rS2mse,rG,rGmse
double precision
1 momsadj
data tol/1.d-10/
data moms(1,1),moms(2,1),moms(3,1)/0.0, 1.0, 0.0/
rG = r_G
rGmse = r_G_mse
do 10 i=2,nsize
call moms_p3(n,ql,qu,moms(1,i-1),moms(1,i))
c
c compute weighted regional mean (M)?
c N.B. Uncertainty in at-site mean is based on previous call to
c p3est_ema() without regional info. A weighted average is
c computed based on the mse of the at-site mean computed
c without regional info and the generalized mean (which
c is defined on a "mean map"
c
if(r_M_mse .gt. 0.d0 .and. r_M_mse .lt. 1.d10) then ! => weighted M
rMmse = r_M_mse
moms(1,i) = (as_M_mse*r_M + rMmse*moms(1,i))/
1 (as_M_mse + rMmse)
else if (r_M_mse .eq. 0.d0) then
moms(1,i) = r_M
else
! moms(2,i) = moms(1,i)
endif
c
c compute weighted regional variance (S2)?
c note: we assume mse of regional estimate proportional to sigma^4
c thus, if VarS2opt is "DF" (default) we adjust rS2mse
c (see notes in Cohn 2011)
c this is a tricky computation, and the arguments are
c non-trivial.
c
c
if(r_S2_mse .ge. 1.d10) then ! "At-Site/STATION"
c moms(2,i) = moms(2,i)
else if(r_S2_mse .lt. 0.d0) then ! "At-Site/STATION"
c moms(2,i) = moms(2,i)
else if(r_S2_mse .eq. 0.d0) then ! "Regional/Generalized"
moms(2,i) = r_S2
else ! "WEIGHTED"
if(VarS2opt .eq. 'DF') then
rS2mse = r_S2_mse*(moms(2,i)/r_S2)**2 ! correct MSE[S] = f(\sigma)
else if(VarS2opt .eq. 'S2') then
rS2mse = r_S2_mse ! no adjustment
else
rS2mse = r_S2_mse ! no adjustment
endif
moms(2,i) = (as_S2_mse*r_S2 + rS2mse*moms(2,i))/
1 (as_S2_mse + rS2mse)
endif
c
c compute weighted regional skew (G)?
c
if(rGmse .le. 0.d0 .and. rGmse .gt. -98.d0) then ! "GENERALIZED, NO MSE"
moms(3,i) = rG
else if (rGmse .gt. 0.d0) then ! "WEIGHTED"
moms(3,i) = (rG*as_G_mse+moms(3,i)*rGmse)/
1 (rGmse+as_G_mse)
else if (rGmse .lt. -98.d0) then ! "STATION SKEW
c moms(3,i) = moms(3,i)
else if (rGmse .ge. 1.d10) then ! "STATION SKEW
c moms(3,i) = moms(3,i)
endif
c
c following call prevents skew from going below -1.41 and also
c ensures that largest observation is within support of fitted distn
c
moms(3,i) = momsadj(n,ql,moms(1,i))
C
C JFE mod 12-DEC-2014 expand looping
C if(i .gt. 1000) then ! eliminate cycles of length 2 or 3
if(i .gt. 10000) then ! eliminate cycles of length 2 or 3
do 50 j=1,3
write(*,*) '(EMA): Convergence criteria not met, i = ',i
write(*,*) ' -- Cycling likely: Correction implemented'
write(*,'(a10,3f10.3)') ' -- M_{i} ',moms(1,i-1)
write(*,'(a10,3f10.3)') ' -- M_{i} ',moms(1,i-1)
moms(j,i) = (moms(j,i) +moms(j,i-1)+moms(j,i-2)+
1 moms(j,i-3)+moms(j,i-4)+moms(j,i-5))/6.d0
50 continue
endif
c
d11(i) = dist_p3(moms(1,i-1),moms(1,i))
c if(d11(i) .le. tol) then ! tac added additional test 15 sep 11
if( (d11(i) .le. tol) .and. (d11(i) .ge. d11(i-1)) ) then
do 20 k=1,3
moms_out(k) = moms(k,i)
20 continue
return
endif
10 continue
write(*,*) ' failure to converge in p3_mom'
do 30 i=1,10
write(*,*) i,(moms(j,i),j=1,3),d11(i)
30 continue
do 40 i=nsize-10,nsize
write(*,*) i,(moms(j,i),j=1,3),d11(i)
40 continue
stop
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine moms_p3
c****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c computes the expected value of a g3 variate with parameters
c given by mc_old(), whose value is known to lie in the interval (ql,qu)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c development history (see above)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c n i*4 number of observations (censored, uncensored, or
c other)
c ql(n) r*8 vector of lower bounds on (log) floods
c qu(n) r*8 vector of upper bounds on (log) floods
c mc_old(3) r*8 vector of p3 parameters
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c output variables:
c ------------------------------------------------------------------------
c
c moms(3) r*8 vector of updated p3 parameters
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine moms_p3(n,ql,qu,mc_old,moms)
implicit none
integer
1 n,nsize,
2 n_e,n_c,bcf,i,j,k
parameter (nsize=25000)
double precision
1 ql(*),qu(*),mc_old(3),moms(3),s_e(3),s_c(3),
2 m_nc_moms(3,nsize),
3 sum,c2,c3,n_bcf,
4 choose,
5 sk0,sk141,skxmax
logical lskewXmax
common /tac002/sk0,sk141,skxmax,lskewXmax,bcf
c note that setting bcf to 0 shuts off bias correction;
c 1997 gets the original Cohn et al. [1997] bcfs
c 2004 gets Griffis et al. [2004] -- the default!
if(n .gt. nsize) then
write(*,*) '(moms_p3): sample size too large ',n
stop
endif
n_e = 0
moms(1) = 0.d0
do 10 i=1,n
if(ql(i) .eq. qu(i)) n_e = n_e+1
if( (i .gt. 1) .and. (ql(i) .eq. ql(max(1,i-1))) .and.
1 (qu(i) .eq. qu(max(1,(i-1)))) ) then
m_nc_moms(1,i) = m_nc_moms(1,i-1)
m_nc_moms(2,i) = m_nc_moms(2,i-1)
m_nc_moms(3,i) = m_nc_moms(3,i-1)
else
call mP3(ql(i),qu(i),mc_old,m_nc_moms(1,i),3)
endif
moms(1) = moms(1)+m_nc_moms(1,i)
10 continue
moms(1) = moms(1)/n
n_c = n - n_e
do 30 j=2,3
s_e(j) = 0.d0
s_c(j) = 0.d0
do 40 i=1,n
if(qu(i) .eq. ql(i)) then
s_e(j) = s_e(j) + ( ql(i) - moms(1) )**j
else
sum = m_nc_moms(j,i) + (-moms(1))**j
do 50 k=1,j-1
sum = sum + choose(j,k)*m_nc_moms(k,i)*(-moms(1))**(j-k)
50 continue
s_c(j) = s_c(j) + sum
endif
40 continue
30 continue
c
c jfe modify to handle all bcf input cases
if(bcf .eq. 1997) then
n_bcf = n_e
c2 = n_bcf/(n_bcf-1.d0)
c3 = ( n_bcf**2)/( (n_bcf-1.d0)*(n_bcf-2.d0) )
else if (bcf .eq. 2004) then
n_bcf = n
c2 = n_bcf/(n_bcf-1.d0)
c3 = ( n_bcf**2)/( (n_bcf-1.d0)*(n_bcf-2.d0) )
else ! no bias correction, all other entered bcf values
n_bcf = 0.d0
c2 = 1.d0
c3 = 1.d0
endif
moms(2) = ( c2*s_e(2) + s_c(2) )/n
moms(3) = ( c3*s_e(3) + s_c(3) )/( n * moms(2)**1.5d0)
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|double precision function dist_p3
c****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c computes "distance" between two p3 parameter sets (converged?)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c development history (see above)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c m1(3) r*8 vector of p3 parameters
c m2(3) r*8 vector of p3 parameters
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c output variables:
c ------------------------------------------------------------------------
c
c dist_p3 r*8 distance between two parameter sets
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
double precision function dist_p3(m1,m2)
implicit none
integer
1 i,ip(3)
double precision
1 m1(3),m2(3),sum
data ip/1,2,0/
sum = 0.d0
do 10 i=1,3
sum = sum + (m1(i)-m2(i))**2/m2(2)**ip(i)/10.**(i-1)
10 continue
dist_p3 = sum
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|double precision function momsadj
c****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c this routine adjusts the skew to ensure two things:
c
c 1. that the ema algorithm converges; for negative skews, with
c left-censored data, there are cases where ema diverges without
c this constraint
c
c 2. that the largest observation in the data set is within the
c support of the fitted distribution
c
double precision function momsadj(n,ql,m)
implicit none
integer
1 n,i,bcf
double precision
1 ql(*),m(3),xmax,parms(3),
2 sk0,sk141,skxmax
logical
1 lskewXmax
common /tac002/sk0,sk141,skxmax,lskewXmax,bcf
xmax = ql(1)
do 10 i=2,n
if(ql(i) .gt. xmax) xmax = ql(i)
10 continue
call m2p(m,parms)
sk0 = m(3)
sk141 = -1.41d0 ! 1: m(3) < -1.41
if(lskewXmax) then
skxmax = 2.d0*sqrt(m(2))/(m(1)-xmax) ! 2: parms(1) < xmax
else
skxmax = sk141
endif
momsadj = max(sk0,sk141,skxmax)
return
end
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c****|double precision function mseg_all
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c computes the mse of station skew for the bulletin 17b/17c analysis
c (see p. 13 B17b)
c
c n.b. b17b recommends using h -- the entire period length --
c for the record length with historical information.
c
c n.b. at_site_option, stored in common, determines how things are
c computed.
c
c at_site_option = 'B17B' => Bulletin 17B MSE formula
c = 'EMA' => First-order EMA MSE
c = 'ADJE' => Adjusted first-order
c
c the 'ADJE' result is identical to the 'B17B' result if there is
c no censored data. Otherwise, 'ADJE' is the adjusted version
c (multiplied by a factor of the ratio
c
c bias_adj = MSE(B17B,syst=Nh)/MSE(EMA,syst=Nh)
c
c timothy a. cohn, 2008
c
c *** do not modify without author''s consent ***
c
c author.......tim cohn
c date.........02 jul 2008
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c nthresh i*4 number of distinct censoring thresholds
c ( (a,b) pairs)
c nobs(*) r*8 vector of number of observations corresponding
c to threshold pair (tl(i),tu(i))
c tl(*) r*8 vector of lower bounds (a)
c tu(*) r*8 vector of upper bounds (b)
c mc(3) r*8 vector of estimated lp3 moments
c
c output variables:
c ------------------------------------------------------------------------
c mseg_all r*8 mse of at-site (station) skew
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
double precision function mseg_all(nthresh,nobs,tl,tu,mc)
implicit none
double precision
1 nobs(*),tl(*),tu(*),mc(3)
double precision mseg,mse_ema,bias_adj,INF(2)
integer
1 nthresh,i,n,n_adj
character*4 at_site_option,at_site_default,at_site_std
common /tacg04/at_site_option,at_site_default,at_site_std
data INF/-99.d0,99.d0/
n = 0
do 10 i=1,nthresh
n = n + nobs(i)
10 continue
c
if(at_site_option .eq. 'B17B') then
mseg_all = mseg(n,mc(3))
else if(at_site_option(1:3) .eq. 'EMA') then
mseg_all = mse_ema(nthresh,nobs,tl,tu,mc,3)
else if(at_site_option .eq. 'ADJE') then
n_adj = min(n,150)
bias_adj = mseg(n_adj,mc(3)) /
1 mse_ema(1,dble(n_adj),INF(1),INF(2),mc,3)
mseg_all = bias_adj * mse_ema(nthresh,nobs,tl,tu,mc,3)
endif
return
end
c****|double precision function mse_ema
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c computes the mse of station skew for an ema analysis
c
c timothy a. cohn, 2008
c
c *** do not modify without author''s consent ***
c
c author.......tim cohn
c date.........1 jul 2008
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c nthresh i*4 number of distinct censoring thresholds
c ( (a,b) pairs)
c nobs(*) r*8 vector of number of observations corresponding
c to threshold pair (tl(i),tu(i))
c tl(*) r*8 vector of lower bounds (a)
c tu(*) r*8 vector of upper bounds (b)
c mc(3) r*8 vector of estimated lp3 moments
c kmom i*4 which moment? (1=mean; 2=variance; 3=skew)
c
c output variables:
c ------------------------------------------------------------------------
c mse_ema r*8 mse of at-site (station) skew
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
double precision function mse_ema(nthresh,nobs,tl,tu,mc,kmom)
implicit none
double precision
1 nobs(*),tl(*),tu(*),mc(3),mc2(3),tl2(100),tu2(100),
2 s_mn(3,3),s_mc(3,3),mn(3),
3 skewmin,tneg,tpos,w
parameter (skewmin=0.06324555)
integer
1 nthresh,i,kmom
c test input value of kmom
if(kmom .gt. 3 .or. kmom .lt. 1) then
write(*,*) 'kmom error ',kmom,' (mse_ema)'
stop
endif
c begin by pseudo-orthogalizing the parameters
mc2(1) = 0.d0
mc2(2) = mc(2)
mc2(3) = mc(3)
do 10 i=1,nthresh
tl2(i) = tl(i) - mc(1)
tu2(i) = tu(i) - mc(1)
10 continue
if(abs(mc2(3)) .gt. skewmin) then ! straight computation
call var_mom(nthresh,nobs,tl2,tu2,mc2,s_mn)
call m2mn(mc2,mn)
call mn2mvarb(mn,s_mn,mc2,s_mc)
mse_ema = s_mc(kmom,kmom)
else ! use weighted sum for skew = skewmin, -skewmin
mc2(3) = -skewmin
call var_mom(nthresh,nobs,tl2,tu2,mc2,s_mn)
call m2mn(mc2,mn)
call mn2mvarb(mn,s_mn,mc2,s_mc)
tneg = s_mc(kmom,kmom)
mc2(3) = skewmin
call var_mom(nthresh,nobs,tl2,tu2,mc2,s_mn)
call m2mn(mc2,mn)
call mn2mvarb(mn,s_mn,mc2,s_mc)
tpos = s_mc(kmom,kmom)
w = (mc(3)-skewmin)/(2.d0*skewmin)
mse_ema = w*tneg + (1.d0-w)*tpos
endif
return
end
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c****|double precision function mseg
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c computes the station skew for the bulletin 17b analysis (see p. 13)
c
c n.b. b17b recommends using h -- the entire period length --
c for the record length with historical information.
c
c copyright, timothy a. cohn, 2000
c
c *** do not modify without author''s consent ***
c
c author.......tim cohn
c date.........11 june 2000
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c n i*4 record length
c g r*8 station skew
c
c output variables:
c ------------------------------------------------------------------------
c mseg r*8 mse of at-site (station) skew
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
double precision function mseg(n,g)
implicit none
double precision g,a,b
integer n
if(abs(g) .le. 0.9) then
a = -0.33 + 0.08*abs(g)
else
a = -0.52 + 0.3 * abs(g)
endif
if(abs(g) .le. 1.5) then
b = 0.94 - 0.26 * abs(g)
else
b = 0.55
endif
mseg = 10**(a - b * log(n/10.d0)/log(10.d0) )
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine ci_ema_m3b
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c m03 is like m02 but uses students t distribution in
c calculation of confidence intervals
c these are the "adjusted" ci-s in cohn, lane and stedinger (wrr 2001)
c
c date..........8 sept 1999 (tac)
c
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ---------------------------------------------------------------------------
c yp r*8 estimated p-th quantile
c cv_yp_syp r*8 estimated cov[yp,syp] (2x2 matrix)
c n.b. syp is sqrt(cvypsyp(1,1))
c s_syp is sqrt(cvypsyp(2,2))
c eps r*8 ci coverages (usually 0.90,0.99,0.999)
c
c
c output variables:
c ------------------------------------------------------------------------
c ci_low r*8 estimated lower critical point of confidence
c interval
c ci_high r*8 estimated upper critical point of confidence
c interval
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine ci_ema_m3b
1 (yp,cv_yp_syp,eps,ci_low,ci_high)
implicit none
save
integer
1 i
double precision
1 yp,cv_yp_syp(2,2),eps,ci_high,ci_low,
4 beta1,c_min,nu,nu_min,p_high,t,var_xsi_d
double precision
1 fp_tnc_icdf
data nu_min/5.0d0/,c_min/0.5d0/ !CTAC was 0.5; 3/19/14 (TAC)
c
c beta1 is coefficient of regression of syp on yp
c
beta1 = cv_yp_syp(1,2)/cv_yp_syp(1,1)
c
c note computation of nu involves not var[syp], but var[syp-beta1*yp]
c
var_xsi_d = cv_yp_syp(2,2) -
1 cv_yp_syp(1,2)**2/cv_yp_syp(1,1)
nu = 0.5d0 * cv_yp_syp(1,1)/var_xsi_d
c
c prevent numerical problems for very small nu (does this arise in practice?)
c
if(nu .le. nu_min) then
write(*,*) 'warning: ci_ema_m3'
write(*,*) ' estimated nu too small',nu
nu = nu_min
write(*,*) ' value replaced with ',nu
endif
c
c compute confidence intervals
c n.b. sign on t means that low t corresponds to high yp
c
p_high = (1.d0+eps)/2.d0
t = fp_tnc_icdf(p_high,nu,0.d0)
ci_high = yp + sqrt(cv_yp_syp(1,1))*t/max(c_min,1.d0-beta1*t)
t = -t
ci_low = yp + sqrt(cv_yp_syp(1,1))*t/max(c_min,1.d0-beta1*t)
return
end
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C*_*-*~*_*-*~* NEW PROGRAM BEGINS HERE *_*-*~*_*-*~*_*-*~
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C****|SUBROUTINE VAR_EMAB
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C GIVEN ESTIMATED PARAMETERS (TAU, ALPHA, BETA) CORR. TO
C CENSORED PEARSON TYPE 3 DATA, THIS PROGRAM COMPUTES EMA
C CONFIDENCE INTERVALS AND OTHER RELEVANT INFO. USING
C COHN''S [2012] METHOD OF INVERSE GAUSSIAN QUADRATURE.
C
C N.B. THESE ARE ALL ASYMPTOTIC RESULTS, BUT SEEM TO PROVIDE
C EXCELLENT RESULTS EVEN IN VERY SMALL SAMPLES. (TAC)
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C DEVELOPMENT HISTORY
C
C TIMOTHY A. COHN 12 OCT 2012
C MODIFIED 27 FEB 2013 (MAJOR REWRITE)
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C INPUT VARIABLES:
C ------------------------------------------------------------------------
C NTH I*4 NUMBER OF DISTINCT CENSORING THRESHOLDS
C ( (A,B) PAIRS)
C NOBS(*) R*8 VECTOR OF NUMBER OF OBSERVATIONS CORRESPONDING
C TO THRESHOLD
C PAIR (A(I),B(I)
C TL(*) R*8 VECTOR OF LOWER BOUNDS (A)
C TU(*) R*8 VECTOR OF UPPER BOUNDS (B)
C MC(3) R*8 VECTOR OF ESTIMATED LP3 MOMENTS
C PQ(*) R*8 VECTOR OF QUANTILES TO BE ESTIMATED
C NQ I*R THE NUMBER OF QUANTILES TO BE ESTIMATED
C EPS R*8 CI COVERAGE TO EMPLOY
C R_S2 R*8 REGIONAL VARIANCE (STD.DEV^2)
C (SEE COHN 2011 NOTEBOOK 2 FOR WHY NEEDED)
C R_M_MSE R*8 MEAN SQUARE ERROR OF REGIONAL MEAN
C R_S2_MSE R*8 MEAN SQUARE ERROR OF REGIONAL VARIANCE
C R_G_MSE R*8 MSE OF G_R (B17) ;
C THIS VARIABLE ENCODES FOUR DISTINCT CASES:
C 1) R_G_MSE = 0 ("GENERALIZED SKEW, NO ERROR")
C USE FIXED G = R_G W/ MSE = 0.0
C 2) -98 < R_G_MSE < 0 ("GENERALIZED SKEW, MSE > 0")
C USE FIXED G = R_G W/ MSE = -R_G_MSE
C 3) 0 < R_G_MSE < 1.D10 ("WEIGHTED SKEW")
C USE G = WEIGHTED AVERAGE OF AT-SITE AND
C REGIONAL SKEW (B17B RECOMMENDATION)
C 4) 1.D10 < R_G_MSE ("STATION SKEW")
C USE G = AT-SITE SKEW
C
C N.B.: G_R, THE REGIONAL SKEWNESS,
C IS SET = SIGN(2,PARMS(3))/SQRT(PARMS(2))
C
C OUTPUT VARIABLES:
C ------------------------------------------------------------------------
C YP(*) R*8 ESTIMATED P-TH QUANTILE
C CV_YP_SYP R*8 3-D MATRIX OF ESTIMATED COV[YP,SYP]
C CIL(*) R*8 VECTOR OF LOWER CONFIDENCE INTS FOR YP
C CIH(*) R*8 VECTOR OF UPPER CONFIDENCE INTS FOR YP
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
SUBROUTINE VAR_EMAB
1 (NTH,NOBS,TL,TU,MC,PQ,NQ,EPS,
2 R_S2, R_M_MSE, R_S2_MSE, R_G_MSE,
4 YP,CV_YP_SYP,CIL,CIH)
IMPLICIT NONE
SAVE
INTEGER
1 PNTH,PNQ,PNNDSUM,PNND1,PNND2,PNND3
PARAMETER (PNTH=4)
PARAMETER (PNND1=2,PNND2=2,PNND3=2)
PARAMETER (PNNDSUM=PNND1*PNND2*PNND3)
INTEGER
1 I,J,K,N,NND(3),NQ,NTH
DOUBLE PRECISION
1 NOBS(*),TL(*),TU(*),PQ(*),EPS,
2 YP(*),CV_YP_SYP(2,2,*),CIL(*),CIH(*),
3 MC(3),S_MC(3,3),
7 R_S2, R_M_MSE, R_S2_MSE, R_G_MSE,
8 GR_MC1(3,PNNDSUM),GR_MC2(3,PNNDSUM,PNNDSUM),
1 W1(PNNDSUM),W2(PNNDSUM,PNNDSUM),
2 QP1(PNNDSUM),QP2(PNNDSUM,PNNDSUM),VP1(PNNDSUM),SP1(PNNDSUM),
3 QP3,COVW
DATA NND/PNND1,PNND2,PNND3/
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C COMPUTE COVARIANCE MATRIX; GRID1; GRID2; RESULTS
C
CALL REGMOMS(NTH,NOBS,TL,TU,MC,
1 R_G_MSE,R_M_MSE,R_S2,R_S2_MSE,S_MC)
CALL GRIDMAKE(MC,S_MC,NND,W1,GR_MC1)
DO 40 I=1,PNNDSUM
CALL REGMOMS(NTH,NOBS,TL,TU,GR_MC1(1,I),
1 R_G_MSE,R_M_MSE,R_S2,R_S2_MSE,S_MC)
CALL GRIDMAKE(GR_MC1(1,I),S_MC,NND,W2(1,I),GR_MC2(1,1,I))
40 CONTINUE
C
DO 50 K=1,NQ
DO 60 I=1,PNNDSUM
QP1(I) = QP3(PQ(K),GR_MC1(1,I))
DO 70 J=1,PNNDSUM
QP2(J,I) = QP3(PQ(K),GR_MC2(1,J,I))
70 CONTINUE
VP1(I) = COVW(PNNDSUM,QP2(1,I),QP2(1,I),W2(1,I))
SP1(I) = SQRT(VP1(I))
60 CONTINUE
YP(K) = QP3(PQ(K),MC)
CV_YP_SYP(1,1,K) = COVW(PNNDSUM,QP1,QP1,W1)
CV_YP_SYP(1,2,K) = COVW(PNNDSUM,QP1,SP1,W1)
CV_YP_SYP(2,1,K) = CV_YP_SYP(1,2,K)
CV_YP_SYP(2,2,K) = COVW(PNNDSUM,SP1,SP1,W1)
CALL CI_EMA_M3B(YP(K),CV_YP_SYP(1,1,K),EPS,CIL(K),CIH(K))
50 CONTINUE
RETURN
END
SUBROUTINE GRIDMAKE(MC,S_MC,NND,W,GR_MC)
C===============================================================================
C
C SUBROUTINE GRIDMAKE COMPUTES A GRID OF PARAMATER TRIPLETS
C GIVEN THE MEAN AND COVARIANCE OF THE PARAMETERS SO THAT
C GAUSSIAN QUADRATURE CAN BE PERFORMED AND THE EXPECTATION
C AND COVARIANCE OF AN ESTIMATOR CAN BE CALCULATED
C FITTED PARAMETERS (M,S2,G), COVARIANCE S_MC
C
C FOR THE ALGEBRA, SEE COHN [2013] (NOTEBOOK 3)
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C INPUT VARIABLES:
C -----------------------------------------------------------------------
C MC(3) R*8 PARAMETERS OF LP3 DISTRIBUTION {M1,M2,M3}
C S_MC(3,3) R*8 COVARIANCE OF NON-CENTRAL MOMENTS
C NND(3) I*4 NUMBER OF NODES IN QUADRATURE ALONG EACH DIMENSION
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C OUTPUT
C ------------------------------------------------------------------------
C W(3) R*8 WEIGHTS TO APPLY TO QUADRATURE SETS
C GR_MC(3,*) R*8 MATRIX OF QUADRATURE TRIPLETS
C
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C AUTHOR....TIM COHN
C DATE......25 FEBRUARY 2013
C
C===============================================================================
C
IMPLICIT NONE
INTEGER PDIM
PARAMETER (PDIM=512)
DOUBLE PRECISION
1 MC(3),S_MC(3,3),
2 T1(PDIM),W1(PDIM),T2(PDIM),W2(PDIM),T3(PDIM),W3(PDIM),
3 GR_MC(3,PDIM),W(PDIM),
4 ALPHA,BETA,Z(3),Z2(3),P(3,3)
INTEGER
1 NND(3),I,J,K,L,IFLAG
C CHECK ARRAY BOUNDS
IF(NND(1)*NND(2)*NND(3) .GT. PDIM) THEN
WRITE(*,*) ' NEED TO INCREASE ARRAY SIZES (PDIM) IN MC2MNVB'
STOP
ENDIF
C INITIALIZE QUADRATURE MODELS; ORTHOGONAL M=0, V=1 QUAD PTS
CALL NORMQUAD(NND(1),T1,W1)
ALPHA = MC(2)**2/S_MC(2,2)
BETA = 1/SQRT(ALPHA)
CALL GAMMAQUAD(NND(2),ALPHA,BETA,T2,W2)
CALL DMADD(-ALPHA*BETA,NND(2),1,T2,NND(2),NND(2),1,T2,NND(2))
CALL NORMQUAD(NND(3),T3,W3)
C CHOLESKY DECOMPOSITION (USED TO INTRODUCE PROPER COVARIANCE)
CALL CHOL33(S_MC,P,IFLAG)
C COMPUTE QUADRATURE VECTOR-SETS AND CORR. WEIGHTS
L = 0
DO 10 K=1,NND(3)
DO 10 J=1,NND(2)
DO 10 I=1,NND(1)
L = L+1
C COMPUTE UNIVARIATE-TRIPLET ORTHOGONAL QUADRATURE POINTS
Z(1) = T1(I)
Z(2) = T2(J)
Z(3) = T3(K)
C USE CHOLESKY P TO PRESERVE TRIPLET VARIANCE/COVARIANCE
CALL DMXTYF(3,3,P,3,3,1,Z,3,3,1,Z2,3)
C ADD MEANS TO PRESERVE CENTRAL MOMENT MEANS
CALL DMSUM(3,1,MC,3,3,1,Z2,3,3,1,GR_MC(1,L),3)
C COMPUTE CORRESPONDING WEIGHTS
W(L) = W1(I)*W2(J)*W3(K)
10 CONTINUE
RETURN
END
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine regmoms(nthresh,nobs,tl,tu,mc,r_G_mse,r_S2,r_S2_mse,s_mc)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c *** do not modify without authors consent ***
c
c author.......tim cohn
c date.........10 feb 2007
c modified...16 jun 2011
c modified...04 apr 2013
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ---------------------------------------------------------------
c nthresh i*4 number of distinct censoring thresholds
c nobs r*8 number of observations corresponding to
c each threshold
c tl(*) r*8 vector of lower bounds (a) of censoring
c tu(*) r*8 vector of upper bounds (b) of censoring
c mc r*8 vector of parameters (first 3 central
c moments of lp3 distribution
c r_G_mse r*8 scalar mse of regional skewness estimator
c N.B. the mse codes for four distinct cases
c 1) mse>0 => weighted skew
c 2) mse=0 => generalized skew (no uncertainty)
c 3) -98< mse <0 => generalized skew (mse = -mse)
c 4) mse < -98 => station skew
c (using r_G_mse = 1.d10 is equivalent)
c r_M_mse r*8 estimated MSE of M
c r_S2 r*8 regional estimate of variance (S^2) (see notes)
c r_S2_mse r*8 estimated MSE of r_S2
c
c output variables:
c ---------------------------------------------------------------
c s_mc(3,3) r*8 matrix of covariance of
c n.b: central parameter estimators
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
subroutine regmoms(
1 nthresh,nobs,tl_in,tu_in,mc_in,
2 r_G_mse,r_M_mse,r_S2,r_S2_mse,s_mc)
implicit none
integer
1 nthresh
double precision
1 nobs(*),tl_in(*),tu_in(*),mc_in(3),r_G_mse,s_mc(3,3),
2 tl(100),tu(100),
2 mc(3),s_mn(3,3),mn(3),wG,r_M,r_M_mse,wM,r_S2,r_S2_mse,rS2mse,wS2
double precision mseg_all
character*4 VarS2opt
common /tacR01/VarS2opt
c set mc(1)=0 to avoid numerical problems (var invariant to loc)
mc(1) = 0.d0
call dmadd(-mc_in(1),nthresh,1,tl_in,nthresh,nthresh,1,tl,nthresh)
call dmadd(-mc_in(1),nthresh,1,tu_in,nthresh,nthresh,1,tu,nthresh)
mc(2) = mc_in(2)
mc(3) = max(-1.5d0,min(1.5d0,mc_in(3)))
call var_mom(nthresh,nobs,tl,tu,mc,s_mn)
call m2mn(mc,mn)
call mn2mvarb(mn,s_mn,mc,s_mc) ! new approach
c
c compute variance of skew; adjust for regional info
c
if(r_G_mse .gt. 0.d0) then ! "WEIGHTED"
wG = r_G_mse/(mseg_all(nthresh,nobs,tl,tu,mc) + r_G_mse)
else if(r_G_mse .ge. -98.d0 .and. r_G_mse .le. 0.d0) then ! "G-w/skew"
wG = 0.d0
else if(r_G_mse .lt. -98.d0) then ! "STATION"
wG = 1.d0
else if(r_G_mse .ge. 1.d10) then ! "STATION"
wG = 1.d0
endif
s_mc(1,3) = wG*s_mc(1,3)
s_mc(3,1) = s_mc(1,3)
s_mc(2,3) = wG*s_mc(2,3)
s_mc(3,2) = s_mc(2,3)
s_mc(3,3) = wG**2*s_mc(3,3) + (1.d0-wG)**2*abs(r_G_mse)
c
c variance of mean (M); adjust for regional info
c
if(r_M_mse .lt. 1.d10 .and. r_M_mse .ge. 0.d0) then ! do nothing?
if(r_M_mse .eq. 0.d0) then ! "Regional/Generalized"
wM = 0.d0
else ! "WEIGHTED"
wM = r_M_mse/(s_mc(1,1)+r_M_mse)
endif
s_mc(1,2) = wM*s_mc(1,2)
s_mc(2,1) = s_mc(1,2)
s_mc(1,3) = wM*s_mc(1,3)
s_mc(3,1) = s_mc(1,3)
s_mc(1,1) = wM**2*s_mc(1,1) + (1.d0-wM)**2*abs(r_M_mse)
endif
c
c variance of variance (standard deviation^2); adjust for regional info
c
if(r_S2_mse .gt. 1.d10) return ! most likely case -- do nothing
if(r_S2_mse .ge. 1.d10) then ! "At-Site/STATION"
wS2 = 1.D0
rS2mse = 1.D10
else if(r_S2_mse .eq. 0.d0) then ! "Regional/Generalized"
wS2 = 0.D0
rS2mse = r_S2_mse
else if(r_S2_mse .lt. 0.d0) then ! "At-Site/STATION"
wS2 = 1.D0
rS2mse = 1.D10
else ! "WEIGHTED"
if(VarS2opt .eq. 'DF') then
rS2mse = r_S2_mse*(mc(2)/r_S2)**2 ! correct MSE[S] = f(\sigma)
else if(VarS2opt .eq. 'S2') then
rS2mse = r_S2_mse ! no adjustment
c else if(VarS2opt .eq. 'S1') then
c rS2mse = ???
else
rS2mse = r_S2_mse ! no adjustment
endif
c !
wS2 = rS2mse/(s_mc(2,2)+rS2mse)
endif
s_mc(1,2) = wS2*s_mc(1,2)
s_mc(2,1) = s_mc(1,2)
s_mc(2,3) = wS2*s_mc(2,3)
s_mc(3,2) = s_mc(2,3)
s_mc(2,2) = wS2**2*s_mc(2,2) + (1.d0-wS2)**2*abs(rS2mse)
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine var_mom
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to compute variance of ema estimator
c
c author.....tim cohn
c date.......4 april 1999
c
c N.B. Regional info now introduced in REGMOMS (TAC...note 10/16/2012)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine var_mom
1 (nthresh,n_in,tl_in,tu_in,mc_in,varm)
implicit none
save
integer
1 nthresh,
2 i,it,j,nth_p
parameter (nth_p=100)
double precision
1 tl_in(nth_p),tu_in(nth_p),mc_in(3),mc(3),
2 mnouta(6),mnoutb(6),mnoutc(6),n_in(nth_p),
3 varm(3,3),a(3,3),ainv(3,3),bc_t(3,3),d(3,3),d_t(3,3),e_x(6),
4 xinf,mu_x(3,3),nh,n_t,t1(3,3),tl,tu,p1,p2,p3,pa,pb,
5 vb(3,3),vb_t(3,3),vc(3,3),vc_t(3,3),
6 skewmin,skewmax
double precision
1 pP3
data xinf/999.d0/
data skewmin/0.06324555/,skewmax/1.41d0/
c limit the mc(1) to avoid potential numerical problems
mc(1) = 0.d0
mc(2) = mc_in(2)
mc(3) = sign(max(skewmin,dabs(mc_in(3))),mc_in(3)) ! limit alpha
mc(3) = sign(min(skewmax,dabs(mc(3))),mc(3)) ! limit skew
call dset(9,0.d0,vb_t,1)
call dset(9,0.d0,vc_t,1)
call dset(9,0.d0,d_t,1)
c
n_t = 0.d0
c
do 10 it = 1,nthresh
c
nh = n_in(it)
n_t = n_t + nh
c
c shift thresholds to reflect using a mean=0
c
tl = tl_in(it) - mc_in(1)
tu = tu_in(it) - mc_in(1)
c
c pa, pb are non-exceedance probabilities
c p1,p2,p3 are probabilities that x<a, a<x<b, x>b
c
pa = pP3(tl,mc)
pb = pP3(tu,mc)
p1 = pa
p2 = pb - pa
p3 = 1.d0 - pb
c
call mP3(-xinf,tl,mc,mnouta,6)
call mP3(tu,xinf,mc,mnoutb,6)
call mP3(tl,tu,mc,mnoutc,6)
do 20 j=1,3
e_x(j) = mnoutc(j)
e_x(j+3) = mnoutc(j+3)
c
mu_x(j,1) = mnouta(j)
mu_x(j,2) = e_x(j)
mu_x(j,3) = mnoutb(j)
20 continue
call varb(mu_x,nh,p1,p2,p3,vb)
call dmsum(3,3,vb,3,3,3,vb_t,3,3,3,vb_t,3)
call varc(e_x,nh,p2,vc)
call dmsum(3,3,vc,3,3,3,vc_t,3,3,3,vc_t,3)
call d_est(nh,mc,pa,pb,d)
call dmsum(3,3,d,3,3,3,d_t,3,3,3,d_t,3)
10 continue
do 30 i=1,3
do 30 j=1,3
if(i .eq. j) then
ainv(i,j) = 1.d0 - d_t(i,j)/n_t
else
ainv(i,j) = -d_t(i,j)/n_t
endif
30 continue
call dlginv(3,ainv,3,a,3)
call dmsum(3,3,vb_t,3,3,3,vc_t,3,3,3,bc_t,3)
call dmrrrr(3,3,a,3,3,3,bc_t,3,3,3,t1,3)
call dmxytf(3,3,t1,3,3,3,a,3,3,3,varm,3)
call dmmult(n_t**(-2),3,3,varm,3,3,3,varm,3)
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine varb
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine varb(mu_x,nh,p1,p2,p3,vb)
implicit none
save
double precision
1 mu_x(3,3),nh,p1,p2,p3,vb(3,3),
2 t1(3,3),vn(3,3)
vn(1,1) = nh*p1*(1.d0-p1)
vn(1,2) = -nh*p1*p2
vn(1,3) = -nh*p1*p3
vn(2,1) = vn(1,2)
vn(2,2) = nh*p2*(1.d0-p2)
vn(2,3) = -nh*p2*p3
vn(3,1) = vn(1,3)
vn(3,2) = vn(2,3)
vn(3,3) = nh*p3*(1.d0-p3)
call dmrrrr(3,3,mu_x,3,3,3,vn,3,3,3,t1,3)
call dmxytf(3,3,t1,3,3,3,mu_x,3,3,3,vb,3)
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine varc
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine varc(e_x,nh,p2,vc)
implicit none
save
integer
1 i,j
double precision
1 e_x(6),nh,p2,vc(3,3),
2 mu_n
mu_n = p2*nh
do 10 i=1,3
do 10 j=1,3
if(i .gt. j) then
vc(i,j) = vc(j,i)
else
vc(i,j) = mu_n*(e_x(i+j) - e_x(i)*e_x(j))
endif
10 continue
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine d_est
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine d_est(nh,mc,pa,pb,d)
implicit none
save
double precision
1 mc(3),nh,parms(3),pa,pb,d(3,3),
2 en1,en3,inf,jacg(3,3),jacl(3,3),pmin,p1,p3,t1,t3
double precision
1 qP3
data inf/1.d19/,pmin/1.d-6/
call m2p(mc,parms)
p1 = pa
p3 = 1.d0 - pb
if(p1 .gt. pmin) then
t1 = qP3(pa,mc)
call expmomderiv(parms,-inf,t1,jacl)
en1 = nh*p1
call dmmult(en1,3,3,jacl,3,3,3,jacl,3)
else
call dset(9,0.d0,jacl,1)
endif
if(p3 .gt. pmin) then
t3 = qP3(pb,mc)
call expmomderiv(parms,t3,inf,jacg)
en3 = nh*p3
call dmmult(en3,3,3,jacg,3,3,3,jacg,3)
else
call dset(9,0.d0,jacg,1)
endif
call dmsum(3,3,jacl,3,3,3,jacg,3,3,3,d,3)
return
end
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
SUBROUTINE MN2MVARB(MN,S_MN,MC,S_MC)
C===============================================================================
C
C SUBROUTINE MN2MVARB COMPUTES THE COVARIANCE MATRIX OF THE FITTED
C PARAMETERS (M,S2,G) OF AN LP3 DISTRIBUTION BASED ON THE COVARIANCE
C OF THE NON-CENTRAL MOMENTS (M1,M2,M3) WHERE Mk=E[X**k]
C
C FOR THE ALGEBRA, SEE COHN [2012] (NOTEBOOK 3)
C
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C INPUT VARIABLES:
C -----------------------------------------------------------------------
C MN(3) R*8 PARAMETERS OF LP3 DISTRIBUTION {M1,M2,M3}
C S_MN(3,3) R*8 COVARIANCE OF NON-CENTRAL MOMENTS
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C OUTPUT
C ------------------------------------------------------------------------
C MC(3) R*8 PARAMETERS OF LP3 DISTRIBUTION {M,S2,G}
C S_MN(3,3) R*8 COVARIANCE OF NON-CENTRAL MOMENTS
C
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C AUTHOR....TIM COHN
C DATE......10 OCTOBER 2012
C
C===============================================================================
C
IMPLICIT NONE
DOUBLE PRECISION
1 MN_IN(3),S_MN_IN(3,3),MC(3),S_MC(3,3),S_MC2(3,3),
2 MN(3),S_MN(3,3),
3 V(3,3),JAC(6,6),JAC_I(6,6),S_MN2(3,3),S_MND(3,3),XDIFF(6),
4 D(6),X(6),X2(6),ERR,TOL
INTEGER
1 NND(3),ITER,I,P_ITMX,IFLAG
PARAMETER (P_ITMX=100)
DATA TOL/1.D-08/,NND/2,2,2/
C INITIALIZE USING A ROUGH ESTIMATE OF S_MC
CALL MN2M_VAR(MN,S_MN,MC,S_MC)
DO 10 ITER=1,P_ITMX
CALL MC2MNVB(MC,S_MC,NND,S_MN2)
CALL JMC2MNVB(MC,S_MC,NND,JAC)
CALL DLGINV(6,JAC,6,JAC_I,6)
CALL DMDIFF(3,3,S_MN,3,3,3,S_MN2,3,3,3,S_MND,3)
CALL TRI_IN(S_MND,XDIFF)
CALL DMRRRR(6,6,JAC_I,6,6,1,XDIFF,6,6,1,D,6)
C
CALL TRI_IN(S_MC,X)
DO 20 I=1,P_ITMX
CALL DMSUM(6,1,X,6,6,1,D,6,6,1,X2,6)
CALL TRI_OUT(X2,S_MC2)
CALL CHOL33(S_MC2,V,IFLAG) ! Step too big?
IF(IFLAG .EQ. 0) THEN ! No -> iterate
GOTO 30
ELSE ! Yes
CALL DMMULT(0.5D0,6,1,D,6,6,1,D,6) ! Try smaller step
ENDIF
20 CONTINUE
WRITE(*,*) 'ERROR IN MN2MVARB'
STOP
30 CONTINUE
CALL DMCOPY(3,3,S_MC2,3,3,3,S_MC,3)
ERR = D(6)**2
IF(I .EQ. 1 .AND. ERR .LE. TOL) THEN ! test convergence wrt skew
GOTO 40 ! exit iff converged and last step was full step (I==1)
ENDIF
10 CONTINUE
40 CONTINUE
RETURN
END
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
SUBROUTINE MC2MNVB(MC,S_MC,NND,S_MN)
C===============================================================================
C
C SUBROUTINE MC2MNVB COMPUTES THE COVARIANCE MATRIX OF THE
C NON-CENTRAL MOMENTS (M1,M2,M3) WHERE Mk=E[X**k]
C OF AN LP3 DISTRIBUTION BASED ON THE COVARIANCE
C OF THE FITTED PARAMETERS (M,S2,G)
C
C FOR THE ALGEBRA, SEE COHN [2012] (NOTEBOOK 3)
C
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C INPUT VARIABLES:
C -----------------------------------------------------------------------
C MC(3) R*8 PARAMETERS OF LP3 DISTRIBUTION {M1,M2,M3}
C S_MC(3,3) R*8 COVARIANCE OF NON-CENTRAL MOMENTS
C NND(3) I*4 NUMBER OF NODES IN QUADRATURE ALONG EACH DIMENSION
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C OUTPUT
C ------------------------------------------------------------------------
C S_MN(3,3) R*8 COVARIANCE OF NON-CENTRAL MOMENTS
C
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C AUTHOR....TIM COHN
C DATE......10 OCTOBER 2012
C
C===============================================================================
C
IMPLICIT NONE
INTEGER PDIM
PARAMETER (PDIM=512)
DOUBLE PRECISION
1 MC(3),S_MC(3,3),S_MN(3,3),
2 MC_P(3,PDIM),W(PDIM),MN_P(3,PDIM),mn_pt(pdim,3),
3 MN_W(3),MN_WT(3),TMP(3),V_WT(3,3),covw
INTEGER
1 NND(3),I,J,K
CALL GRIDMAKE(MC,S_MC,NND,W,MC_P)
DO 10 K=1,NND(1)*NND(2)*NND(3)
CALL M2MN(MC_P(1,K),MN_P(1,K))
DO 10 I=1,3
MN_PT(K,I) = MN_P(I,K)
10 CONTINUE
DO 20 I=1,3
DO 20 J=1,3
S_MN(I,J) = COVW(NND(1)*NND(2)*NND(3),MN_PT(1,I),MN_PT(1,J),W)
20 CONTINUE
RETURN
END
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
SUBROUTINE JMC2MNVB(MC,S_MC,NND,JAC)
C===============================================================================
C
C SUBROUTINE JMC2MNVB COMPUTES THE MATRIX OF THE
C NON-CENTRAL VARIANCES (S_MN) AS A FUNCTION OF THE "TRIANGULAR"
C CENTRAL MOMENTS (S_MC)
C
C N.B. THE INPUT MATRICES ARE IN FULL; THE RESULT IS EXPRESSED
C IN A VECTOR/TRIANGULAR FORM (6 DISTINCT ELEMENTS)
C
C FOR THE ALGEBRA, SEE COHN [2012] (NOTEBOOK 3)
C
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C INPUT VARIABLES:
C -----------------------------------------------------------------------
C MC(3) R*8 PARAMETERS OF LP3 DISTRIBUTION {M1,M2,M3}
C S_MC(3,3) R*8 COVARIANCE OF NON-CENTRAL MOMENTS
C NND(3) I*4 NUMBER OF NODES IN QUADRATURE ALONG EACH DIMENSION
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C OUTPUT
C ------------------------------------------------------------------------
C JAC(6,6) R*8 JACOBIAN
C
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C AUTHOR....TIM COHN
C DATE......10 OCTOBER 2012
C
C===============================================================================
C
IMPLICIT NONE
DOUBLE PRECISION
1 MC(3),S_MC(3,3),JAC(6,6),ERROR,ACC,EPS,DELTA,
2 XMIN,XMAX,MCT,S_MCT,S
INTEGER
1 I,J,IFAIL,NND(3),NND_OUT,STERM(6)
EXTERNAL FJTACD
COMMON /TACJ012/MCT(3),S_MCT(3,3),I,J,NND_OUT(3)
DATA EPS/0.D0/,ACC/0.D0/,DELTA/0.0001D0/,STERM/2,3,1,4,2,0/
CALL IMCOPY(3,1,NND,3,3,1,NND_OUT,3)
CALL DMCOPY(3,1,MC,3,3,1,MCT,3)
CALL DMCOPY(3,3,S_MC,3,3,3,S_MCT,3)
S = SQRT(MC(2))
DO 10 I=1,6 ! I INDEXES PC VAR WRT DERIV OF PN COMPUTED
DO 10 J=1,6 ! J INDEXES PN VAR WHOSE CHANGE IS TO BE COMPUTED
XMAX = DELTA * S**STERM(I) ! Covariance ~ S^I
XMIN = -XMAX
CALL DIFF2(1,0.D0,XMIN,XMAX,FJTACD,EPS,ACC,JAC(J,I),ERROR,IFAIL) !q&d
c CALL DIFFRE(1,0.D0,XMIN,XMAX,FJTACD,EPS,ACC,JAC(J,I),ERROR,IFAIL) !
10 CONTINUE
RETURN
END
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
DOUBLE PRECISION FUNCTION FJTACD(X)
C===============================================================================
C
C FJTACD COMPUTES JACOBIAN OF SIGMA(M1,M2,M3) WRT SIGMA(M,S2,G)
C
C FOR ALGEBRA, SEE COHN [2012] (NOTEBOOK 3)
C
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C INPUT VARIABLES:
C -----------------------------------------------------------------------
C X R*8 INPUT ARGUMENT
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
IMPLICIT NONE
INTEGER I,J,NND
DOUBLE PRECISION
1 X,MC,S_MC,S_MCT(3,3),S_MN(3,3),PC(6),PN(6)
COMMON /TACJ012/MC(3),S_MC(3,3),I,J,NND(3)
CALL TRI_IN(S_MC,PC)
PC(I) = PC(I) + X
CALL TRI_OUT(PC,S_MCT)
CALL MC2MNVB(MC,S_MCT,NND,S_MN)
CALL TRI_IN(S_MN,PN)
FJTACD = PN(J)
RETURN
END
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
SUBROUTINE TRI_IN(S,T)
C===============================================================================
C
C SUBROUTINE TRI_IN EXTRACTS THE UNIQUE ELEMENTS FROM A SYMMETRIC
C 3X3 MATRIX AND PUTS THEM INTO A VECTOR
C
C SUBROUTINE TRI_OUT REVERSES THE TRANSFORMATION
C
C FOR THE ALGEBRA, SEE COHN [2012] (NOTEBOOK 3)
C
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C INPUT VARIABLES:
C -----------------------------------------------------------------------
C S(3,3) R*8 COVARIANCE OF NON-CENTRAL MOMENTS
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C OUTPUT
C ------------------------------------------------------------------------
C T(6) R*8 VECTOR OF ELEMENTS
C
C
C****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
C
C AUTHOR....TIM COHN
C DATE......10 OCTOBER 2012
C
C===============================================================================
IMPLICIT NONE
DOUBLE PRECISION S(3,3),T(6)
T(1) = S(1,1)
T(2) = S(2,1)
T(3) = S(3,1)
T(4) = S(2,2)
T(5) = S(2,3)
T(6) = S(3,3)
RETURN
END
C===============================================================================
SUBROUTINE TRI_OUT(T,S)
DOUBLE PRECISION S(3,3),T(6)
S(1,1) = T(1)
S(2,1) = T(2)
S(3,1) = T(3)
S(1,2) = S(2,1)
S(2,2) = T(4)
S(3,2) = T(5)
S(1,3) = S(3,1)
S(2,3) = S(3,2)
S(3,3) = T(6)
RETURN
END
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine mn2m_var(mn,s_mn,mc,s_mc)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to convert variance in mn (non-central moments)
c into variance in m (central moments)
c
c author.....tim cohn
c date.......12 june 2000
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c mn = non-central moments
c s_mn(3,3) = variance-covariance matrix of mn
c mc = central moments
c s_mc(3,3) = variance-covariance matrix of mc
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine mn2m_var(mn,s_mn,mc,s_mc)
implicit none
save
double precision
1 m1,m2,m3,mn(3),s_mn(3,3),mc(3),s_mc(3,3),
2 df(3,3),temp(3,3)
c
c 1.a compute central moments from non-central moments
c
m1 = mn(1)
m2 = mn(2)
m3 = mn(3)
call mn2m(mn,mc)
c
c 1.b compute jacobian of central moments with respect to non-central
c moments
c n.b. df(2,1) = d(mc[2])/d(m[1])
c
df(1,1) = 1.d0
df(1,2) = 0.d0
df(1,3) = 0.d0
df(2,1) = -2.d0*m1
df(2,2) = 1.d0
df(2,3) = 0.d0
df(3,1) = (6.d0*m1**2 - 3*m2)/(-m1**2 + m2)**1.5 +
1 (3.d0*m1*(2.d0*m1**3 - 3.d0*m1*m2 + m3))/
2 (-m1**2 + m2)**2.5
df(3,2) = (-3.d0*m1)/(-m1**2 + m2)**1.5 -
1 (3.d0*(2.d0*m1**3 - 3.d0*m1*m2 + m3))/
2 (2.d0*(-m1**2 + m2)**2.5)
df(3,3) = (-m1**2 + m2)**(-1.5)
c
c 1.c compute asymptotic covariance of central moments
c df.s_m.df
c
call dmrrrr(3,3,df,3,3,3,s_mn,3,3,3,temp,3)
call dmxytf(3,3,temp,3,3,3,df,3,3,3,s_mc,3)
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine m2mn_var
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to convert variance in mn (non-central moments)
c into variance in m (central moments)
c
c author.....tim cohn
c date.......12 june 2000
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c mc = central moments
c s_mc(3,3) = variance-covariance matrix of mc
c mn = non-central moments
c s_mn(3,3) = variance-covariance matrix of mn
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine m2mn_var(mc,s_mc,mn,s_mn)
implicit none
save
double precision
1 mc1,mc2,mc3,mn(3),s_mn(3,3),mc(3),s_mc(3,3),
2 dr(3,3),temp(3,3)
mc1 = mc(1)
mc2 = mc(2)
mc3 = mc(3)
call m2mn(mc,mn)
c
c 4.a compute jacobian of non central moments with respect to central
c moments
c
dr(1,1) = 1.d0
dr(1,2) = 0.d0
dr(1,3) = 0.d0
dr(2,1) = 2.d0*mc1
dr(2,2) = 1.d0
dr(2,3) = 0.d0
dr(3,1) = 3.d0*mc1**2 + 3.d0*mc2
dr(3,2) = 3.d0*mc1 + (3.d0*sqrt(mc2)*mc3)/2.d0
dr(3,3) = mc2**1.5
c
c 4.b compute asymptotic covariance of central moments df.s_m.df
c
call dmrrrr(3,3,dr,3,3,3,s_mc,3,3,3,temp,3)
call dmxytf(3,3,temp,3,3,3,dr,3,3,3,s_mn,3)
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|program testrs
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c *** delete first-column c and compile with imslfake.f and probfun.f
c routines to run test on all of the enclosed subroutines
c
c
c author.....tim cohn
c date.......2 feb 2007
c
c program testrs;call testroutines();end
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine mP3(tl,tu,m,mnout,n)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to compute the expected value of the k-th moment of
c a pearson type 3 variate between tl and tu with moments m=(mu,sigma^2,g)
c
c author.....tim cohn
c date.......2 feb 2007
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine mP3(tl,tu,m,mnout,n)
implicit none
integer
1 n,
2 i,j,k
double precision
1 tl,tu,t,m(3),mnout(*),
2 a(0:3),b(0:12,0:36),expz(0:36),fp(0:36),fwh(0:36),
3 mg(36),mwh(36),parms(3),
4 mu,s,g,tau,zl,zu,pdfu,pdfl,cdfu,cdfl,
5 w,wg,wwh,zl1,zu1,
6 choose,fp_g2_mom_trc,fp_z_pdf,fp_z_cdf,whlp2z
data b/481*0.d0/,mg/36*0.d0/,mwh/36*0.d0/
mu = m(1)
s = sqrt(m(2))
g = m(3)
zl = max(-1d20,min(1d20,whlp2z((tl-mu)/s,g)))
zu = max(-1d20,min(1d20,whlp2z((tu-mu)/s,g)))
cdfu = fp_z_cdf(zu)
cdfl = fp_z_cdf(zl)
c
c test to see if we have an interval to consider
c n.b. if interval is off support of f, use end closest to
c support as observed value
c
if(cdfu .eq. cdfl) then
if(abs(tl-mu) .lt. abs(tu-mu)) then
t = tl
else
t = tu
endif
do 5 k=1,n
mnout(k) = t**k
5 continue
return
endif
if(n .gt. 12) then
write(*,*) 'mP3: error; n too large: ',n
stop
endif
c
c compute relative weight to apply to gamma solution vs wilson hilferty
c
w = max(0.d0,(abs(g)-0.0007)/(0.0010-0.0007))
if(w .ge. 1.d0) then
wwh = 0.d0
else
wwh = (1.d0+cos(3.14159265359*w))/2.d0
endif
wg = 1.d0-wwh
c
c compute moments for abs(g)>0.07 (i.e. large skew) with inc. gamma function
c
if(wg .gt. 0.d0) then
call m2p(m,parms)
tau = parms(1)
fp(0) = 1.d0
do 10 i=1,n
fp(i) = fp_g2_mom_trc(parms(2),tl-tau,tu-tau,i)
mg(i) = fp(i)
do 10 j=0,i-1
mg(i) = mg(i) + choose(i,j)*tau**(i-j)*fp(j)
10 continue
endif
c
c compute moments for small skews using wilson-hilferty transformation
c n.b. a() vector contains power series expansion
c f(x,g) = f(z) where x=a.(1,z,z^2,z^3)
c where x is standardized gamma with skew g
c
c first compute moments of z given zl < z < zu
c
if(wwh .gt. 0.d0) then
pdfu = fp_z_pdf(zu)
pdfl = fp_z_pdf(zl)
expz(0) = 1.d0
expz(1) = (-pdfu+pdfl)/(cdfu-cdfl)
if(cdfu .lt. 1.d0) then
zu1 = zu
else
zu1 = 0.d0
endif
if(cdfl .gt. 0.d0) then
zl1 = zl
else
zl1 = 0.d0
endif
do 15 i=2,3*n
expz(i) = (-(zu1**(i-1))*pdfu+(zl1**(i-1))*pdfl)/(cdfu-cdfl)
1 + (i-1) * expz(i-2)
15 continue
c
c now define a() [coefficients in series expansion of wilson-hilferty trans.]
c
a(0) = -g*(3888.-108.*g**2+g**4)/23328.
a(1) = (1-g**2/36)**2
a(2) = (g/6.)*(1-g**2/36.)
a(3) = g**2/108.
b(0,0) = 1.d0
c
c compute coefficients in expected value of censored x
c
fwh(0) = 1.d0
do 20 i=1,n
fwh(i) = 0.d0
do 20 j=0,3*i
b(i,j) = 0.d0
do 30 k=max(0,j-3*(i-1)),min(j,3)
b(i,j) = b(i,j) + b(i-1,j-k)*a(k)
30 continue
fwh(i) = fwh(i) + b(i,j)*expz(j)
20 continue
c
c de-standardize results (i.e. add in mu and multiply by sigma as approp.)
c
do 35 i=1,n
mwh(i) = s**i*fwh(i)
do 35 j=0,i-1
mwh(i) = mwh(i) + choose(i,j)*mu**(i-j)*s**j*fwh(j)
35 continue
else
do 37 i=1,n
mwh(i) = 0.0
37 continue
endif
c
c compute weighted sum
c
do 40 i=1,n
mnout(i) = wg*mg(i) + wwh*mwh(i)
40 continue
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
double precision function whlp2z(x,g)
double precision x,g
if(g .eq. 0.d0) then
whlp2z = x
else
whlp2z = (6.d0/g)*(g**2/36.d0-1.d0+max(0.d0,1.d0+g*x/2.d0)**
1 (1.d0/3.d0))
endif
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
double precision function whz2lp(z,g)
double precision z,g
if(g .eq. 0.d0) then
whz2lp = z
else
whz2lp = (2.d0/g)*(1.d0+g*z/6.d0-g**2/36.d0)**3-2.d0/g
endif
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
double precision function dp3(x,m)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to compute the pdf at x of
c a pearson type 3 variate with moments m=(mu,sigma^2,g)
c
c author.....tim cohn
c date.......2 feb 2007
c
implicit none
double precision
1 x,m(3),
2 parms(3),g,mu,s,z,
3 w,wg,wwh,dp3g,dp3wh,
4 fp_g3_pdf,fp_z_pdf,whlp2z
g = m(3)
c
c compute relative weight to apply to gamma solution vs wilson hilferty
c
w = max(0.d0,(abs(g)-0.0007)/(0.0010-0.0007))
if(w .ge. 1.d0) then
wwh = 0.d0
else
wwh = (1.d0+cos(3.14159265359*w))/2.d0
endif
wg = 1.d0-wwh
c
c compute cdf for abs(g)>0.07 (i.e. large skew) with inc. gamma function
c
if(wg .gt. 0.d0) then
call m2p(m,parms)
dp3g = fp_g3_pdf(x,parms)
endif
c
c compute cdf for small skews using wilson-hilferty transformation
c
if(wwh .gt. 0.d0) then
mu = m(1)
s = sqrt(m(2))
z = whlp2z((x-mu)/s,g)
dp3wh = fp_z_pdf(z) * (1.d0/s) * (1+(g*(x-mu)/s)/2.)**(-2./3.)
endif
c
c compute weighted sum
c
dp3 = wg*dp3g + wwh*dp3wh
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
double precision function pP3(x,m)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to compute the cdf at x of
c a pearson type 3 variate with moments m=(mu,sigma^2,g)
c
c author.....tim cohn
c date.......2 feb 2007
c
implicit none
double precision
1 x,m(3),
2 parms(3),g,mu,s,z,
3 w,wg,wwh,pP3g,pP3wh,
4 fp_g3_cdf,fp_z_cdf,whlp2z
g = m(3)
c
c compute relative weight to apply to gamma solution vs wilson hilferty
c
w = max(0.d0,(abs(g)-0.0007)/(0.0010-0.0007))
if(w .ge. 1.d0) then
wwh = 0.d0
else
wwh = (1.d0+cos(3.14159265359*w))/2.d0
endif
wg = 1.d0-wwh
c
c compute cdf for abs(g)>0.07 (i.e. large skew) with inc. gamma function
c
if(wg .gt. 0.d0) then
call m2p(m,parms)
pP3g = fp_g3_cdf(x,parms)
endif
c
c compute cdf for small skews using wilson-hilferty transformation
c
if(wwh .gt. 0.d0) then
mu = m(1)
s = sqrt(m(2))
z = whlp2z((x-mu)/s,g)
pP3wh = fp_z_cdf(z)
endif
c
c compute weighted sum
c
pP3 = wg*pP3g + wwh*pP3wh
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
double precision function qP3(q,m)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to compute the inverse cdf of
c a pearson type 3 variate with moments m=(mu,sigma^2,g)
c
c author.....tim cohn
c date.......2 feb 2007
c
implicit none
double precision
1 q,m(3),
2 parms(3),g,mu,s,
3 w,wg,wwh,qP3g,qP3wh,
4 fp_g3_icdf,fp_z_icdf,whz2lp,infinity
data infinity/1.0d31/
g = m(3)
if(q .le. 0.d0) then
if(g .gt. 0.d0) then
call m2p(m,parms)
qP3 = parms(1)
else
qp3 = -infinity
return
endif
else if(q .ge. 1.d0) then
if(g .lt. 0.d0) then
call m2p(m,parms)
qP3 = parms(1)
else
qp3 = +infinity
return
endif
endif
c
c compute relative weight to apply to gamma solution vs wilson hilferty
c
w = max(0.d0,(abs(g)-0.0007)/(0.0010-0.0007))
if(w .ge. 1.d0) then
wwh = 0.d0
else
wwh = (1.d0+cos(3.14159265359*w))/2.d0
endif
wg = 1.d0-wwh
c
c compute cdf for abs(g)>0.07 (i.e. large skew) with inc. gamma function
c
if(wg .gt. 0.d0) then
call m2p(m,parms)
qP3g = fp_g3_icdf(q,parms)
else
qP3g = 0.0
endif
c
c compute cdf for small skews using wilson-hilferty transformation
c
if(wwh .gt. 0.d0) then
mu = m(1)
s = sqrt(m(2))
qP3wh = mu+s*whz2lp(fp_z_icdf(q),g)
else
qP3wh = 0.0
endif
c
c compute weighted sum
c
qP3 = wg*qP3g + wwh*qP3wh
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|subroutine rP3
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to compute a sample of random pearson type 3
c variates with moments m=(mu,sigma^2,g)
c
c author.....tim cohn
c date.......2 feb 2007
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c N.B. To initialize:
c call srand(iseed)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
double precision function rP3(m)
implicit none
double precision
1 m,qP3
real rand
rP3 = qP3(dble(rand()),m)
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c program testrs;call testroutines();end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
subroutine testroutines()
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c program to test the following routines
c pP3(x,m) -- cdf of lp3
c qP3(p,m) -- inverse cdf of lp3
c dp3(x,m) -- pdf of lp3
c mP3(...) -- non-central moments of lp3
c
c
c author.....tim cohn
c date.......2 feb 2007
c
implicit none
integer
1 ng,np,
2 i,j,k,
3 ier,neval,
4 limit,lenw,last,iwork(100000),k1
parameter
1 (ng=15,np=11)
external ftest01
double precision
1 pp(0:np),gg(ng),m,
2 x,p,abserr,fp(0:3),kk,mnout(3),
3 work(400000),
3 qP3,pP3
data pp/0.0000001,0.001,0.010,0.050,0.100,0.250,0.500,
1 0.7500,0.900,0.950,0.990,0.999/
data gg/-3.0,-2.0,-1.0,-0.50,-0.10,-0.07,-0.01,0.,
1 0.01,0.07,0.10,0.5,1.0,2.0,3.0/
data limit,lenw/100000,400000/
common /zap111/m(3),kk
write(*,*) 'testing qP3,pP3'
write(*,'(6a14)') ' g',' mu',' s^2',' pp',' p',' x'
write(*,*)
abserr = 0.d0
do 10 i=1,ng
do 10 j=1,np
do 10 k=0,1
m(1) = 0.+k
m(2) = 1.+k
m(3) = gg(i)
x = qP3(pp(j),m)
p = pP3(x,m)
abserr = max(abserr,abs(p-pp(j)))
if(abs(p-pp(j)) .gt. 1e-6) then
write(*,'(4f14.4,3e14.5)') m(3),m(1),m(2),pp(j),p,x
endif
10 continue
write(*,*)
write(*,*) ' probabilities tested:'
write(*,'(7f8.4,/)') pp
write(*,*)
write(*,*) ' skews tested:'
write(*,'(7f8.4,/)') gg
write(*,*)
write(*,*) ' maximum absolute error in probability:'
write(*,'(1f18.8/)') abserr
c
write(*,*)
write(*,*) ' *** checking the censored moments ***'
write(*,*)
m(1) = 2.54
m(2) = 1.66
do 20 i=1,ng
m(3) = gg(i)
do 20 j=1,np
call mP3(qP3(pp(j-1),m),qP3(pp(j),m),m,mnout,3)
write(*,'(4f10.4,3e14.5)') m(3),m(1),m(2),pp(j),mnout
do 30 k=0,3
kk=k
call dqag(ftest01,qP3(pp(j-1),m),qP3(pp(j),m),
1 1.d-6,1.d-6,2,fp(k),abserr,neval,ier,
2 limit,lenw,last,iwork,work)
if(ier .ne. 0) write(*,*) ' ier (dqag) = ',ier
if(k .gt. 0) fp(k)=fp(k)/fp(0)
30 continue
write(*,'(40x,3e14.5)') (fp(k1),k1=1,3)
write(*,'(10x,3f10.6,3e14.2)')
1 pp(j-1),pp(j),
2 fp(0),
3 (fp(k1)/mnout(k1)-1.d0,k1=1,3)
20 continue
stop
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
double precision function ftest01(x)
implicit none
double precision x,m,kk,arg,dp3
common /zap111/m(3),kk
if(kk .eq. 0.d0) then
arg = 1
else
arg = x**kk
endif
ftest01 = arg*dp3(x,m)
return
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c****|subroutine compress2
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c compresses the threshold data to reduce redundant computation
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c development history
c
c timothy a. cohn 20 sep 2007
c modified 31 dec 2003
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ------------------------------------------------------------------------
c n i*4 number of observations (censored, uncensored, or
c other)
c tl(n) r*8 vector of lower bounds on (log) floods
c tu(n) r*8 vector of upper bounds on (log) floods
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c output variables:
c ------------------------------------------------------------------------
c
c nt i*4 number of distinct censoring thresholds
c nobs(nt) r*8 number of observations corresponding to
c threshold
c tl2(nt) r*8 lower bounds on (log) flood threshold
c tu2(nt) r*8 upper bounds on (log) flood threshold
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
subroutine compress2(n,tl,tu,nt,n2,tl2,tu2)
integer
1 n,nt
double precision
1 tl(*),tu(*),n2(*),tl2(*),tu2(*)
nt = 0
do 10 i=1,n
do 20 j=1,nt
if(tl(i) .eq. tl2(j) .and. tu(i) .eq. tu2(j)) then
n2(j) = n2(j)+1.d0
goto 10
endif
20 continue
nt = nt+1
n2(nt) = 1.d0
tl2(nt) = tl(i)
tu2(nt) = tu(i)
10 continue
n2(nt+1) = 0
do 30 i=1,nt
n2(nt+1) = n2(nt+1)+n2(i)
30 continue
return
end
subroutine b17cip(n,moms,pq,peps,cil,ciu)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c computes confidence intervals used by B17B
c
c tim cohn........24 Nov 2003
c ........19 feb 2007 (changed call to use moms, not parms)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ---------------------------------------------------------------------------
c n i*4 number of observations (censored, uncensored, or other)
c moms(3) r*8 fitted parameters of lp3 distribution
c pq r*8 flood probability (usually 0.99)
c peps r*8 confidence interval coverage for two-sided ci
c (peps = 0.90 corresponds to a two-sided coverage of 0.90)
c cil r*8 left-hand end of log-space ci
c ciu r*8 right-hand end of log-space ci
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
implicit none
integer
1 n
double precision
1 pq,peps,cil,ciu,
2 moms(3),klpc,kupc
call b17ci(n,moms(3),pq,(1.d0+peps)/2.d0,klpc,kupc)
cil = moms(1) + klpc * sqrt(moms(2))
ciu = moms(1) + kupc * sqrt(moms(2))
return
end
subroutine b17ci(n,skew,p,c,klpc,kupc)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c computes confidence intervals used by B17B
c
c tim cohn........24 Nov 2003
c ........19 feb 2007
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c input variables:
c ---------------------------------------------------------------------------
c n i*4 number of observations (censored, uncensored, or other)
c skew r*8 skewness of fitted lp3 distribution
c p r*8 flood non-exceedance probability (usually 0.99)
c c r*8 confidence interval coverage for one-sided ci
c (c = 0.90 corresponds to a two-sided coverage of 0.90)
c klpc r*8 left-hand factor for ci
c kupc r*8 right-hand factor for ci
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c note that a 90% ci will be constructed by calling:
c
c call b17ci(n,g,0.99d0,0.90d0,klpc,kupc)
c
c then the log-space ci is
c (xbar + s * klpc, xbar + s * kupc)
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
implicit none
integer
1 n
double precision
1 skew,p,c,klpc,kupc,
2 zc,kgwp,a,b,
3 fp_z_icdf,kfxx
zc = fp_z_icdf(c)
kgwp = kfxx(skew,p)
a = 1.d0 - zc**2/(2.d0*(n-1.d0))
b = kgwp**2 - zc**2/n
kupc = (kgwp + sqrt(kgwp**2 - a*b))/a
klpc = (kgwp - sqrt(kgwp**2 - a*b))/a
return
end
double precision function kfxx(skew,prob)
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c computes critical points of LP3 distribution
c returns "K" value in format used by B17B
c
c tim cohn........19 feb 2007
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
implicit none
double precision
1 skew,prob,m(3),qp3
data m/0,1,0/
m(3) = skew
kfxx = qp3(prob,m)
return
end
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c n.b. remove the "c" at start of next line to test the program
c program testit; call testsub001; return; end
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c this represents the test case given on page 9-3 of B17B
c
c correct result is:
c klpc, kupc 2.059 3.026
c lci, uci 3.515 3.757
c cil, ciu 3.515 3.757
c
subroutine testsub001
implicit none
integer
1 n
double precision
1 parms(3),moms(3),p,c,klpc,kupc,l,u
moms(1) = 3.d0
moms(2) = (0.25d0)**2
moms(3) = 0.20d0
call m2p(moms,parms)
n = 50
p = 0.99d0
c = 0.90d0
call b17ci(n,moms(3),p,c,klpc,kupc)
write(*,'(a,2f10.3)') 'klpc, kupc',klpc,kupc
l = moms(1) + sqrt(moms(2))*klpc
u = moms(1) + sqrt(moms(2))*kupc
write(*,'(a,2f10.3)') 'lci, uci ',l,u
call m2p(moms,parms)
call b17cip(n,parms,p,2*c-1.d0,l,u)
write(*,'(a,2f10.3)') 'cil, ciu ',l,u
stop
end
c*_*-*~*_*-*~* new program begins here *_*-*~*_*-*~*_*-*~
blockdata emablk
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
c author.....tim cohn
c date.......27 feb 2008
c
c****|===|====-====|====-====|====-====|====-====|====-====|====-====|==////////
c
implicit none
double precision
1 gbcrit,gbthresh,alph01,alph10,pvaluew,qs,
2 sk0,sk141,skxmax,pqd,eps
integer
1 ns,nlow,nzero,bcf,nqd
character*4
1 at_site_option,at_site_default,at_site_std,gbtype,VarS2opt
logical lskewXmax
logical cirun
common /tac002/sk0,sk141,skxmax,lskewXmax,bcf
common /tacg04/at_site_option,at_site_default,at_site_std
C JFE common /tacg01/gbcrit,gbthresh,pvaluew(10000),qs(10000),
common /tacg01/gbcrit,gbthresh,pvaluew(20000),qs(20000),
1 ns,nlow,nzero,gbtype
common /tacmg1/alph01,alph10
common /tacdgb/cirun
common /tacpq1/pqd(100),nqd
common /tacci1/eps
common /tacR01/VarS2opt
data at_site_option/'ADJE'/
data at_site_default/'ADJE'/
data at_site_std/'ADJE'/
data cirun/.TRUE./
data alph01/0.01d0/,alph10/0.10d0/
data sk141/-1.41d0/
data lskewXmax/.FALSE./
data bcf/1997/
c data bcf/2004/
data VarS2opt/'DF'/
C
C JFE Mod 27-FEB-2016
C JFE nqd = number of quantiles estimated, see nq=nqd
C JFE use as a control on extrapolation
data nqd/41/
c data nqd/32/
C
C JFE Mod and notes 18-MAR-2015
C
C pqd is dim 100
C Tim sends 32 legit values, then does initialization for remaining
C 100 -32 =68, which explains last line
C JFE Mod - we will modify and expand this block data
C can use a new variable, such as pqd1, pqd2, with an if statement on input?
C would need a common block in peakfqSA noting what data block to read
C this way, user specifies how far to go. Could also consider loop control
C need to track nqd
C
C JFE Mod 27-FEB-2016
C
C JFE expand probabilities for quantiles, variances and CI calculations
C JFE pqd is dimension 100; last line initializes the remaining
C
data pqd/0.0001,0.0005,0.001 ,0.002 ,0.005 ,0.010 ,0.020 ,0.025 ,
1 0.040 ,0.050 ,0.100 ,0.200 ,0.300 ,0.3333,0.400 ,0.4296,
2 0.5 ,0.5708,0.600 ,0.700 ,0.800 ,0.900 ,0.950 ,0.960 ,
3 0.975 ,0.980 ,0.990 ,0.995 ,0.998 ,0.999 ,0.9995,0.9999,
4 0.99995,0.99998,0.99999,0.999995,0.999998,0.999999,
5 0.9999995,0.9999998,0.9999999, 59*99.000/
C
C JFE original input by TAC
C data pqd/0.0001,0.0005,0.001 ,0.002 ,0.005 ,0.010 ,0.020 ,0.025 ,
C 1 0.040 ,0.050 ,0.100 ,0.200 ,0.300 ,0.3333,0.400 ,0.4296,
C 2 0.5 ,0.5708,0.600 ,0.700 ,0.800 ,0.900 ,0.950 ,0.960 ,
C 3 0.975 ,0.980 ,0.990 ,0.995 ,0.998 ,0.999 ,0.9995,0.9999,
C 4 68*99.000/
C JFE epsilon width for confidence intervals
C JFE this is currently a scalar input
C JFE 0.90 is a 90% CI width, returning 5 and 95% confidence limits
data eps/0.90d0/
C
end