lmomco (version 1.7.3)

pdfgpa: Probability Density Function of the Generalized Pareto Distribution

Description

This function computes the probability density of the Generalized Pareto distribution given parameters ($\xi$, $\alpha$, and $\kappa$) of the distribution computed by pargpa. The probability density function of the distribution is

$$f(x) = \alpha^{-1} e^{-(1-\kappa)y} \mbox{,}$$ where $y$ is

$$y = -\kappa^{-1} \log\left(1 - \frac{\kappa(x-\xi)}{\alpha}\right) \mbox{ for } \kappa \ne 0 \mbox{, and}$$

$$y = (x-\xi)/A \mbox{ for } \kappa = 0 \mbox{,}$$ where $f(x)$ is the probability density for quantile $x$, $\xi$ is a location parameter, $\alpha$ is a scale parameter, and $\kappa$ is a shape parameter.

Usage

pdfgpa(x, para)

Arguments

x

A real value.

para

The parameters from pargpa or similar.

Value

• Probability density ($f$) for $x$.

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

cdfgpa, quagpa, pargpa

Examples

lmr <- lmom.ub(c(123,34,4,654,37,78))
  gpa <- pargpa(lmr)
  x <- quagpa(0.5,gpa)
  pdfgpa(x,gpa)