cdfkap: Kappa distribution

In lmom: L-Moments

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))

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.

Value

cdfkap gives the distribution function; quakap gives the quantile function.

Note

The functions expect the distribution parameters in a vector, rather than as separate arguments as in the standard R distribution functions pnorm, qnorm, etc.

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.

Examples

# 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))

lmom documentation built on Oct. 1, 2024, 1:08 a.m.