quagev: Quantile Function of the Generalized Extreme Value Distribution

Description

This function computes the quantiles of the Generalized Extreme Value distribution given parameters ($\xi$, $\alpha$, and $\kappa$) of the distribution computed by pargev. The quantile function of the distribution is

$$x(F) = \xi + \frac{\alpha}{\kappa} \left( 1-(-\log(F))^\kappa \right) \mbox{ for } \kappa \ne 0 \mbox{ and }$$

$$x(F) = \xi - \alpha \log(-\log(F)) \mbox{ for } \kappa = 0 \mbox{,}$$

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

quagev(f, para, paracheck=TRUE)

Arguments

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

para

The parameters from pargev or similar.

paracheck

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

Value

Quantile value for nonexceedance probability $F$.

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, vol. 52, p. 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.

Examples

Run this code

lmr <- lmom.ub(c(123,34,4,654,37,78))
  quagev(0.5,pargev(lmr))