Probability Density Function of the Kappa Distribution

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Description

This function computes the probability density of the Kappa distribution given parameters (ξ, α, κ, and h) computed by parkap. The probability density function is

f(x) = α^{-1} [1-κ(x - ξ)/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 or nonexceedance probability at x, ξ is a location parameter, α is a scale parameter, and κ is a shape parameter.

Usage

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pdfkap(x, para)

Arguments

x

A real value vector.

para

The parameters from parkap or vec2par.

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, lmomkap, parkap

Examples

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

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