quakap: Quantile Function of the Kappa Distribution
Description
This function computes the quantiles of the Kappa distribution given parameters (\(\xi\), \(\alpha\), \(\kappa\), and \(h\)) computed by parkap. The quantile function is
$$x(F) = \xi + \frac{\alpha}{\kappa}\left(1-{\left(\frac{1-F^h}{h}\right)}^\kappa\right) \mbox{,}$$
where \(x(F)\) is the quantile for nonexceedance probability \(F\), \(\xi\) is a location parameter, \(\alpha\) is a scale parameter, \(\kappa\) is a shape parameter, and \(h\) is another shape parameter.
Usage
quakap(f, para, paracheck=TRUE)
Value
Quantile value for nonexceedance probability \(F\).
Arguments
f
Nonexceedance probability (\(0 \le F \le 1\)).
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.
Author
W.H. Asquith
References
Hosking, J.R.M., 1994, The four-parameter kappa distribution: IBM Journal of Reserach and Development, v. 38, no. 3, pp. 251--258.
Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.