| cdfkap {lmom} | 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 |
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))