pdfkap {lmomco}R Documentation

Probability Density Function of the Kappa Distribution

Description

This function computes the probability density of the Kappa distribution given parameters (xi, α, kappa, and h) of the distribution computed by pargev. The probability density function of the distribution is

f(x) &= α^{-1} [1-kappa(x - xi)/α]^{1/k-1} times [F(x)]^{1-h}

where f(x) is the probability density for quantile x, F(x) is the cumulative distribution function of the distribution (cdfkap)), xi is a location parameter, α is a scale parameter, and kappa is a shape parameter.

Usage

pdfkap(x, para)

Arguments

x A real value.
para The parameters from parkap or similar.

Value

Probability density (f) for x.

Author(s)

W.H. Asquith

References

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

Sourced from written communication with Dr. Hosking in October 2007.

See Also

cdfkap, quakap, parkap

Examples

kap <- vec2par(c(1000,15000,0.5,-0.4),type='kap')
F <- nonexceeds()
x <- quakap(F,kap)
check.pdf(pdfkap,kap,plot=TRUE)

[Package lmomco version 0.96.3 Index]