# pdfgpa: Probability Density Function of the Generalized Pareto... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function computes the probability density of the Generalized Pareto distribution given parameters (ξ, α, and κ) computed by pargpa. The probability density function is

f(x) = α^{-1} \exp(-(1-κ)Y) \mbox{,}

where Y is

Y = -κ^{-1} \log≤ft(1 - \frac{κ(x-ξ)}{α}\right)\mbox{,}

for κ \ne 0, and

Y = (x-ξ)/α\mbox{,}

for κ = 0, where f(x) is the probability density for quantile x, ξ is a location parameter, α is a scale parameter, and κ is a shape parameter.

## Usage

 1 pdfgpa(x, para) 

## Arguments

 x A real value vector. para The parameters from pargpa or vec2par.

## Value

Probability density (f) for x.

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.

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.

cdfgpa, quagpa, lmomgpa, pargpa
 1 2 3 4  lmr <- lmoms(c(123,34,4,654,37,78)) gpa <- pargpa(lmr) x <- quagpa(0.5,gpa) pdfgpa(x,gpa)