Cumulative Distribution Function of the Gumbel Distribution

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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.

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

pdfgum, quagum, lmomgum, pargum

Examples

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

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