regtst(regdata, nsim=1000)regdata containing the input data.
It should be a data frame, each of whose rows contains data for one site.
The first seven columns should contain respectively
the site name,"regtst", which is a list with elements as follows.regdat.nsim."wak") fitted to the regional weighted average
$L$-moment ratios.Dcrit)
for smaller regions.
Three heterogeneity measures are calculated, each based on
a different measure of between-site dispersion of $L$-moment ratios:
[1] weighted standard deviation of $L$-CVs;
[2] average of $L$-CV/$L$-skew distances;
[3] average of $L$-skew/$L$-kurtosis distances.
These dispersion measures are the quantities $V$, $V_2$,
and $V_3$ defined respectively in equations (4.4), (4.6), and (4.7)
of Hosking and Wallis (1997).
The heterogeneity measures are calculated from them as in
equation (4.5) of Hosking and Wallis (1997).
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 the accuracy of quantile estimates.
Goodness of fit is evaluated for five candidate distributions:
generalized logistic,
generalized extreme value,
generalized normal (lognormal),
Pearson type III (3-parameter gamma), and
generalized Pareto.
In the output the distributions are referred to by 3-letter abbreviations,
respectively glo, gev, gno, pe3, and gpa.
If the region is homogeneous and data at different sites are
statistically independent, then if one of the distributions is
the true distribution for the region its goodness-of-fit measure
should have approximately a standard normal distribution.
Provided that the region is acceptably close to homogeneous,
the fit may be judged acceptable at the 10 per cent significance level
if the $Z$ value is less than 1.645 (i.e., qnorm(0.95)) in absolute value.
Calculation of heterogeneity and goodness-of-fit measures
involves the sampling variability of $L$-moment ratios
in a homogeneous region whose record lengths and
average $L$-moment ratios match those of the data.
The sampling variability is estimated by Monte Carlo simulation
using nsim replications of the region.
Results will vary between invocations of regtst
with different seeds for the random-number generator.summary.regtst for summaries.# An example from Hosking (1996). Compare the output with
# the file 'cascades.out' in the LMOMENTS Fortran package at
# http://lib.stat.cmu.edu/lmoments/general (results will not
# be identical, because random-number generators are different).
data(Cascades)
summary(regtst(Cascades, nsim=500))
# Output from 'regsamlmu' can be fed straight into 'regtst'
data(Maxwind)
regtst(regsamlmu(Maxwind))Run the code above in your browser using DataLab