lmomco (version 2.3.7)

quagpa: Quantile Function of the Generalized Pareto Distribution

Description

This function computes the quantiles of the Generalized Pareto distribution given parameters (\(\xi\), \(\alpha\), and \(\kappa\)) computed by pargpa. The quantile function is $$x(F) = \xi + \frac{\alpha}{\kappa} \left( 1-(1-F)^\kappa \right)\mbox{,}$$ for \(\kappa \ne 0\), and $$x(F) = \xi - \alpha\log(1-F)\mbox{,}$$ for \(\kappa = 0\), where \(x(F)\) is the quantile for nonexceedance probability \(F\), \(\xi\) is a location parameter, \(\alpha\) is a scale parameter, and \(\kappa\) is a shape parameter.

Usage

quagpa(f, para, paracheck=TRUE)

Value

Quantile value for nonexceedance probability \(F\).

Arguments

f

Nonexceedance probability (\(0 \le F \le 1\)).

para

The parameters from pargpa or vec2par.

paracheck

A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Author

W.H. Asquith

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

cdfgpa, pdfgpa, lmomgpa, pargpa

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  quagpa(0.5,pargpa(lmr))
if (FALSE) {
# Let us compare L-moments, parameters, and 90th percentile for a simulated
# GPA distibution of sample size 100 having the following parameters between
# lmomco and lmom packages in R. The answers are the same.
gpa.par <- lmomco::vec2par(c(1.02787, 4.54603, 0.07234), type="gpa")
X <- lmomco::rlmomco(100, gpa.par)
lmom::samlmu(X)
lmomco::lmoms(X)
lmom::pelgpa(lmom::samlmu(X))
lmomco::pargpa(lmomco::lmoms(X))
lmom::quagpa(0.90, lmom::pelgpa(lmom::samlmu(X)))
lmomco::quagpa(0.90, lmomco::pargpa(lmomco::lmoms(X)))}