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))
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).
Value
cdfkap gives the distribution function;
quakap gives the quantile function.
Details
The kappa distribution with
location parameter $\xi$,
scale parameter $\alpha$ and
shape parameters $k$ and $h$
has quantile function
$$x(F)=\xi-{\alpha\over k}(1-({1-F^h \over h})^k).$$
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.
See Also
cdfglo for the generalized logistic distribution,
cdfgev for the generalized extreme-value distribution,
cdfgpa for the generalized Pareto distribution,
cdfgum for the Gumbel distribution,
cdfexp for the exponential distribution.