lmomco (version 2.4.14)

pdfwak: Probability Density Function of the Wakeby Distribution

Description

This function computes the probability density of the Wakeby distribution given parameters (\(\xi\), \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\)) computed by parwak. The probability density function is $$f(x) = (\alpha[1-F(x)]^{\beta - 1} + \gamma[1-F(x)]^{-\delta - 1})^{-1}\mbox{,}$$ where \(f(x)\) is the probability density for quantile \(x\), \(F(x)\) is the cumulative distribution function or nonexceedance probability at \(x\), \(\xi\) is a location parameter, \(\alpha\) and \(\beta\) are scale parameters, and \(\gamma\), and \(\delta\) are shape parameters. The five returned parameters from parwak in order are \(\xi\), \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\).

Usage

pdfwak(x, para)

Value

Probability density (\(f\)) for \(x\).

Arguments

x

A real value vector.

para

The parameters from parwak or vec2par.

Author

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

cdfwak, quawak, lmomwak, parwak

Examples

if (FALSE) {
lmr <- vec2lmom(c(1,0.5,.4,.3,.15))
wak <- parwak(lmr)
F <- nonexceeds()
x <- quawak(F,wak)
check.pdf(pdfwak,wak,plot=TRUE)
}