quagum: Quantile Function of the Gumbel Distribution

In wasquith/lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Quantile Function of the Gumbel Distribution

Description

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

x(F) = \xi - \alpha\log(-\log(F)) \mbox{,}

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

Usage

quagum(f, para, paracheck=TRUE)

Arguments

f	Nonexceedance probability (0 \le F \le 1).
para	The parameters from pargum 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, 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

cdfgum, pdfgum, lmomgum, pargum

Examples

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

wasquith/lmomco documentation built on Nov. 13, 2024, 4:53 p.m.