cdfgpa {lmomco}R Documentation

Cumulative Distribution Function of the Generalized Pareto Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Generalized Pareto distribution given parameters (xi, α, and kappa) of the distribution computed by pargpa. The cumulative distribution function of the distribution is

F(x) = 1 - e^{-y} mbox{,}

where y is

y = -kappa^{-1} log(1 - frac{kappa(x-xi)}{α}) mbox{ for } kappa ne 0 mbox{, and}

y = (x-xi)/A mbox{ for } kappa = 0 mbox{,}

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

Usage

cdfgpa(x, para)

Arguments

x A real value.
para The parameters from pargpa or similar.

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, vol. 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

quagpa, pargpa

Examples

  lmr <- lmom.ub(c(123,34,4,654,37,78))
  cdfgpa(50,pargpa(lmr))

[Package lmomco version 0.96.3 Index]