quagev {lmomco}

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, and

x(F) = \xi - \alpha \log(-\log(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. The range of x is -\infty < x \le \xi + \alpha/\kappa if k > 0; \xi + \alpha/\kappa \le x < \infty if \kappa \le 0. Note that the shape parameter \kappa parameterization of the distribution herein follows that in tradition by the greater L-moment community and others use a sign reversal on \kappa. (The evd package is one example.)

Usage

quagev(f, para, paracheck=TRUE)

Arguments

f

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

para

The parameters from pargev 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.

Value

Quantile value for nonexceedance probability F.

Author(s)

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, doi:10.1111/j.2517-6161.1990.tb01775.x.

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

cdfgev, pdfgev, lmomgev, pargev

Examples

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