# cdfkap: Kappa distribution In lmom: L-Moments

 cdfkap R Documentation

## 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.

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.
# Random sample from the kappa distribution