Probability Density Function of the Generalized Pareto Distribution

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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

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pdfgpa(x, para)

Arguments

x

A real value vector.

para

The parameters from pargpa or vec2par.

Value

Probability density (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.

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

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

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