lmomco (version 2.4.14)

quagum: 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)

Value

Quantile value for nonexceedance probability \(F\).

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.

Author

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))