cdfgpa {lmomco}

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, \alpha, and \kappa) computed by pargpa. The cumulative distribution function is

F(x) = 1 - \mathrm{exp}(-Y) \mbox{,}

where Y is

Y = -\kappa^{-1} \log\left(1 - \frac{\kappa(x-\xi)}{\alpha}\right)\mbox{,}

for \kappa \ne 0 and

Y = (x-\xi)/\alpha\mbox{,}

for \kappa = 0, where F(x) is the nonexceedance probability for quantile x, \xi is a location parameter, \alpha is a scale parameter, and \kappa is a shape parameter. The range of x is \xi \le x \le \xi + \alpha/\kappa if k > 0; \xi \le x < \infty if \kappa \le 0. Note that the shape parameter \kappa parameterization of the distribution herein follows that in tradition by the greater L-moment community and others use a sign reversal on \kappa. (The evd package is one example.)

Usage

cdfgpa(x, para)

Arguments

x

A real value vector.

para

The parameters from pargpa 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, doi:10.1111/j.2517-6161.1990.tb01775.x.

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

pdfgpa, quagpa, lmomgpa, pargpa

Examples

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