cdfkap: Kappa distribution

Description

Distribution function and quantile function of the kappa distribution.

Usage

cdfkap(x, para = c(0, 1, 0, 0))
quakap(f, para = c(0, 1, 0, 0))

Value

cdfkap gives the distribution function;

quakap gives the quantile function.

Arguments

x: Vector of quantiles.
f: Vector of probabilities.
para: Numeric vector containing the parameters of the distribution, in the order $\xi, \alpha, k, h$ (location, scale, shape, shape).

Details

The kappa distribution with location parameter $\xi$, scale parameter $\alpha$ and shape parameters $k$ and $h$ has quantile function $$x(F)=\xi+{\alpha\over k}\biggl\lbrace1-\biggl({1-F^h \over h}\biggr)^k\biggr\rbrace.$$

Its special cases include the generalized logistic ($h=-1$), generalized extreme-value ($h=0$), generalized Pareto ($h=1$), logistic ($k=0$, $h=-1$), Gumbel ($k=0$, $h=0$), exponential ($k=0$, $h=1$), and uniform ($k=1$, $h=1$) distributions.

References

Hosking, J. R. M. (1994). The four-parameter kappa distribution. IBM Journal of Research and Development, 38, 251-258.

Hosking, J. R. M., and Wallis, J. R. (1997). Regional frequency analysis: an approach based on L-moments, Cambridge University Press, Appendix A.10.

Examples

Run this code

# Random sample from the kappa distribution
# with parameters xi=0, alpha=1, k=-0.5, h=0.25.
quakap(runif(100), c(0,1,-0.5,0.25))

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