lmomco (version 2.4.14)

cdfgpa: 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 $$F(x)=1-\exp (-Y)\text{,}$$ where $Y$ is $$Y=-{\kappa }^{-1}\log (1-\frac{\kappa (x-\xi )}{\alpha })\text{,}$$ for $\kappa \ne 0$ and $$Y=(x-\xi )/\alpha \text{,}$$ 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 $k>0$; $\xi \le x<\mathrm{\infty }$ 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)

Value

Nonexceedance probability ($F$) for $x$.

Arguments

x

A real value vector.

para

The parameters from pargpa or vec2par.

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, pp. 105--124, tools:::Rd_expr_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))