lmomco (version 2.3.1)

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 \(\kappa\)) computed by pargpa. The probability density function is $$f(x) = \alpha^{-1} \exp(-(1-\kappa)Y) \mbox{,}$$ 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 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 vector.

para

The parameters from pargpa or vec2par.

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, 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

cdfgpa, quagpa, lmomgpa, pargpa

Examples

# NOT RUN {
  lmr <- lmoms(c(123,34,4,654,37,78))
  gpa <- pargpa(lmr)
  x <- quagpa(0.5,gpa)
  pdfgpa(x,gpa)
# }