pdfgev {lmomco}R Documentation

Probability Density Function of the Generalized Extreme Value Distribution

Description

This function computes the probability density of the Generalized Extreme Value distribution given parameters (xi, α, and kappa) of the distribution computed by pargev. The probability density function of the distribution is

f(x) = α^{-1} e^{-(1-kappa)y - e^{-y}} mbox{,}

y = -kappa^{-1} log(1 - frac{kappa(x-xi)}{α}) mbox{ for } kappa ne 0 mbox{, and}

y = (x-xi)/α mbox{ for } kappa = 0 mbox{,}

where f(x) is the probability density for quantile x, xi is a location parameter, α is a scale parameter, and kappa is a shape parameter.

Usage

pdfgev(x, para)

Arguments

x A real value.
para The parameters from pargev or similar.

Value

Probability density (f) for x.

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, 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.

See Also

pdfgev, quagev, pargev

Examples

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

[Package lmomco version 0.96.3 Index]