# cdfgum: Cumulative Distribution Function of the Gumbel Distribution In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function computes the cumulative probability or nonexceedance probability of the Gumbel distribution given parameters (ξ and α) computed by pargum. The cumulative distribution function is

F(x) = \mathrm{exp}(-\mathrm{exp}(Y)) \mbox{,}

where

Y = -\frac{x - ξ}{α} \mbox{,}

where F(x) is the nonexceedance probability for quantile x, ξ is a location parameter, and α is a scale parameter.

## Usage

 1 cdfgum(x, para) 

## Arguments

 x A real value vector. para The parameters from pargum or vec2par.

## Value

Nonexceedance probability (F) for x.

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.

pdfgum, quagum, lmomgum, pargum
 1 2  lmr <- lmoms(c(123,34,4,654,37,78)) cdfgum(50,pargum(lmr))