lmomco (version 2.3.1)

pargpa: Estimate the Parameters of the Generalized Pareto Distribution

Description

This function estimates the parameters of the Generalized Pareto distribution given the L-moments of the data in an ordinary L-moment object (lmoms) or a trimmed L-moment object (TLmoms for t=1). The relations between distribution parameters and L-moments are seen under lmomgpa or lmomTLgpa.

Usage

pargpa(lmom, zeta=1, xi=NULL, checklmom=TRUE, ...)

Arguments

lmom

An L-moment object created by lmoms, TLmoms with trim=0, or vec2lmom.

zeta

The right censoring fraction. If less than unity then a dispatch to the pargpaRC is made and the lmom argument must contain the B-type L-moments. If the data are not right censored, then this value must be left alone to the default of unity.

xi

The lower limit of the distribution. If \(\xi\) is known, then alternative algorithms are used.

checklmom

Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the \(\tau_4\) and \(\tau_3\) inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check.

...

Other arguments to pass.

Value

An R list is returned.

type

The type of distribution: gpa.

para

The parameters of the distribution.

source

The source of the parameters: “pargpa”.

References

Hosking, J.R.M., 1990, L-moments---Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105--124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

See Also

lmomgpa, cdfgpa, pdfgpa, quagpa

Examples

# NOT RUN {
X   <- rexp(200)
lmr <- lmoms(X)
P1  <- pargpa(lmr)
P2  <- pargpa(lmr, xi=0.25)

# }
# NOT RUN {
F <- nonexceeds()
plot(pp(X), sort(X))
lines(F,quagpa(F,P1))  # black line
lines(F, quagpa(F,P2), col=2)   # red line
# }