quakap: Quantile Function of the Kappa Distribution

Description

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

x(F) = ξ + \frac{α}{κ}≤ft(1-{≤ft(\frac{1-F^h}{h}\right)}^κ\right) \mbox{,}

where x(F) is the quantile for nonexceedance probability F, ξ is a location parameter, α is a scale parameter, κ is a shape parameter, and h is another shape parameter.

Usage

 1 quakap(f, para, paracheck=TRUE) 

Arguments

 f Nonexceedance probability (0 ≤ F ≤ 1). para The parameters from parkap or vec2par. paracheck A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Value

Quantile value for nonexceedance probability F.

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.

cdfkap, pdfkap, lmomkap, parkap
 1 2  lmr <- lmoms(c(123,34,4,654,37,78,21,32,231,23)) quakap(0.5,parkap(lmr))