The original Fortran routine by Hosking is here used to analyse a region.
HW.original (data, cod, Nsim=500)
# S3 method for HWorig
print (x, ...)
# S3 method for HWorig
plot (x, interactive=TRUE, ...)
LMR (PARA, distr="EXP")
PEL (XMOM, distr="EXP")
SAMLMR (X, A=0, B=0)
SAMLMU (X)
SAMPWM (X, A=0, B=0)
REGLMR (data, cod)
REGTST (data, cod, A=0, B=0, Nsim=500)object of class HWorig
vector representing data from many samples defined with cod
array that defines the data subdivision among sites
number of regions simulated with the bootstrap of the original region
logical: if TRUE the graphic showing is interactive
additional parameter for print
parameters of the distribution (vector)
distribution:
EXP = Exponential (2 parameters: xi, alfa);
GAM = Gamma (2 parameters: alfa, beta);
GEV = Generalized extreme value (3 parameters: xi, alfa, k);
GLO = Generalized logistic (3 parameters: xi, alfa, k);
GNO = Generalized Normal (3 parameters: xi, alfa, k);
GPA = Generalized Pareto (3 parameters: xi, alfa, k);
GUM = Gumbel (2 parameters: xi, alfa);
KAP = Kappa (4 parameters: xi, alfa, k, h);
NOR = Normal (2 parameters: mu, sigma);
PE3 = Pearson type III (3 parameters: mu, sigma, gamm);
WAK = Wakeby (5 parameters: xi, alfa, beta, gamm, delta).
the L-moment ratios of the distribution, in order \(\lambda_1\), \(\lambda_2\), \(\tau_3\), \(\tau_4\), \(\tau_5\)...
a data vector
Parameters of plotting position: for unbiased estimates (of the \(\lambda\)'s) set A=B=zero. Otherwise, plotting-position estimators are used, based on the plotting position \((j+a)/(n+b)\) for the \(j\)'th smallest of \(n\) observations. For example, A=-0.35 and B=0.0 yields the estimators recommended by Hosking et al. (1985, technometrics) for the GEV distribution.
HW.original returns an object of class HWorig (what the Fortran subroutine REGTST return).
LMR calculates the L-moment ratios of a distribution given its parameters.
PEL calculates the parameters of a distribution given its L-moments.
SAMLMR calculates the sample L-moments ratios of a data-set.
SAMLMU calculates the `unbiased' sample L-moments ratios of a data-set.
SAMPWM calculates the sample probability weighted moments of a data-set.
REGLMR calculates regional weighted averages of the sample L-moments ratios.
REGTST calculates statistics useful in regional frequency analysis.
1) Discordancy measure, d(i), for individual sites in a region.
Large values might be used as a flag to indicate potential errors
in the data at the site. "large" might be 3 for regions with 15
or more sites, but less (exact values in array dc1) for smaller
regions.
2) Heterogeneity measures, H(j), for a region based upon either:-
j=1: the weighted s.d. of the l-cvs or
j=2: the average distance from the site to the regional average
on a graph of l-cv vs. l-skewness
j=3: the average distance from the site to the regional average
on a graph of l-skewness vs. l-kurtosis.
In practice H(1) is probably sufficient. a value greater than
(say) 1.0 suggests that further subdivision of the region should
be considered as it might improve quantile estimates.
3) Goodness-of-fit measures, Z(k), for 5 candidate distributions:
k=1: generalized logistic
k=2: generalized extreme value
k=3: generalized normal (lognormal)
k=4: pearson type iii (3-parameter gamma)
k=5: generalized pareto.
Provided that the region is acceptably close to homogeneous,
the fit may be judged acceptable at 10
if Z(k) is less than 1.645 in absolute value.
For further details see Hosking and Wallis (1997), "Regional frequency analysis: an approach based on L-moments", cambridge university press, chapters 3-5.
Documentation of the original Fortran routines by Hosking available at http://www.research.ibm.com/people/h/hosking/lmoments.html.
Differences among HW.original and HW.tests should depend on differences among PEL and par.kappa for the kappa distribution.
A numerical algorithm is used to resolve the implicit Equations (A.99) and (A.100) in Hosking and Wallis (1997, pag. 203-204).
The algorithms in PEL and par.kappa are different.
Anyway the risults of the tests should converge asymptotically.
IBM software disclaimer
LMOMENTS: Fortran routines for use with the method of L-moments
Permission to use, copy, modify and distribute this software for any purpose and without fee is hereby granted, provided that this copyright and permission notice appear on all copies of the software. The name of the IBM Corporation may not be used in any advertising or publicity pertaining to the use of the software. IBM makes no warranty or representations about the suitability of the software for any purpose. It is provided "AS IS" without any express or implied warranty, including the implied warranties of merchantability, fitness for a particular purpose and non-infringement. IBM shall not be liable for any direct, indirect, special or consequential damages resulting from the loss of use, data or projects, whether in an action of contract or tort, arising out of or in connection with the use or performance of this software.
# NOT RUN {
data(hydroSIMN)
annualflows
summary(annualflows)
x <- annualflows["dato"][,]
cod <- annualflows["cod"][,]
split(x,cod)
HW.original(x,cod)
fac <- factor(annualflows["cod"][,],levels=c(34:38))
x2 <- annualflows[!is.na(fac),"dato"]
cod2 <- annualflows[!is.na(fac),"cod"]
HW.original(x2,cod2)
plot(HW.original(x2,cod2))
# }
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