Kappa distribution
Distribution function and quantile function of the kappa distribution.
cdfkap(x, para = c(0, 1, 0, 0)) quakap(f, para = c(0, 1, 0, 0))
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). |
The kappa distribution with location parameter xi, scale parameter alpha and shape parameters k and h has quantile function
x(F) = xi + alpha (1 - ( (1-F^h)/h )^k) / 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.
cdfkap gives the distribution function;
quakap gives the quantile function.
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
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.
# 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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