pdfgum {lmomco}

Probability Density Function of the Gumbel Distribution

Description

This function computes the probability density of the Gumbel distribution given parameters (\xi and \alpha) computed by pargum. The probability density function is

f(x) = \alpha^{-1} \exp(Y)\,\exp[-\exp(Y)]\mbox{,}

where

Y = -\frac{x - \xi}{\alpha} \mbox{,}

where f(x) is the nonexceedance probability for quantile x, \xi is a location parameter, and \alpha is a scale parameter.

Usage

pdfgum(x, para)

Arguments

x

A real value vector.

para

The parameters from pargum or vec2par.

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, 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

cdfgum, quagum, lmomgum, pargum

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  gum <- pargum(lmr)
  x <- quagum(0.5,gum)
  pdfgum(x,gum)