regsimh {lmomRFA} | R Documentation |
Estimates, using Monte Carlo simulation, the distribution of heterogeneity and goodness-of-fit measures for regional frequency analysis. These are the statistics H and Z^{DIST} defined respectively in sections 4.3.3 and 5.2.3 of Hosking and Wallis (1997).
regsimh(qfunc, para, cor = 0, nrec, nrep = 500, nsim = 500)
qfunc |
List containing the quantile functions for each site. Can also be a single quantile function, which will be used for each site. |
para |
Parameters of the quantile functions at each site.
If qfunc is a list, para must be a list of the same
length whose components are numeric vectors, the parameters of
the corresponding component of qfunc .
If qfunc is a single quantile function, para can be
a single vector, containing a single set of parameter values
that will be used for each site;
a matrix or data frame whose rows each contain the
parameter values for one site;
or a list of length length(nrec) whose components are
numeric vectors, each containing the parameter values for one site. |
cor |
Specifies the correlation matrix of the frequency distribution of each site's data. Can be a matrix (which will be rescaled to a correlation matrix if necessary) or a constant (which will be taken as the correlation between each pair of sites). |
nrec |
Numeric vector containing the record lengths at each site. |
nrep |
Number of simulated regions. |
nsim |
Number of simulations used, within each of the nrep
simulated regions, when calculating heterogeneity and
goodness-of-fit measures. |
A realization is generated of data simulated from
the region specified by parameters qfunc
, para
, and cor
,
and with record lengths at each site specified by argument nrec
.
The simulation procedure is as described in Hosking and Wallis (1997),
Table 6.1, through step 3.1.2.
Heterogeneity and goodness-of-fit measures are computed
for the realization, using the same method as in function regtst
.
The entire procedure is repeated nrep
times, and the values
of the heterogeneity and goodness-of-fit measures are saved.
Average values, across all nrep
realizations,
of the heterogeneity and goodness-of-fit measures are computed.
An object of class "regsimh"
.
This is a list with the following components:
nrep |
The number of simulated regions (argument nrep ). |
nsim |
The number of simulation used within each region
(argument nsim ). |
results |
Matrix of dimension 8 by nrep ,
containing the values, for each of the nrep simulated regions,
of the heterogeneity and goodness-of-fit measures. |
means |
Vector of length 8, containing the mean values,
across the nrep simulated regions,
of the three heterogeneity and five goodness-of-fit measures. |
J. R. M. Hosking hosking@watson.ibm.com
Hosking, J. R. M., and Wallis, J. R. (1997). Regional frequency analysis: an approach based on L-moments. Cambridge University Press.
regtst
for details of the
heterogeneity and goodness-of-fit measures.
## Not run: data(Cascades) # A regional data set rmom<-regavlmom(Cascades) # Regional average L-moments # Set up an artificial region to be simulated: # -- Same number of sites as Cascades # -- Same record lengths as Cascades # -- Mean 1 at every site (results do not depend on the site means) # -- L-CV varies linearly across sites, with mean value equal # to the regional average L-CV for the Cascades data. # 'LCVrange' specifies the range of L-CV across the sites. # -- L-skewness the same at each site, and equal to the regional # average L-skewness for the Cascades data nsites <- nrow(Cascades) means <- rep(1,nsites) LCVrange <- 0.025 LCVs <- seq(rmom[2]-LCVrange/2, rmom[2]+LCVrange/2, len=nsites) Lskews<-rep(rmom[3], nsites) # Each site will have a generalized normal distribution: # get the parameter values for each site pp <- t(apply(cbind(means, means*LCVs ,Lskews), 1, pelgno)) # Set correlation between each pair of sites to 0.64, the # average inter-site correlation for the Cascades data avcor <- 0.64 # Run the simulation. It will take some time (about 1 minute # on a Lenovo T60, a moderately fast 2006-vintage laptop) # Note that the results are consistent with the statement # "the average H value of simulated regions is 1.08" # in Hosking and Wallis (1997, p.98). set.seed(123) regsimh(qfunc=quagno, para=pp, cor=avcor, nrec=Cascades$n, nrep=100) ## End(Not run)