Distribution function and quantile function
of the Wakeby distribution.
Usage
cdfwak(x, para = c(0, 1, 0, 0, 0))
quawak(f, para = c(0, 1, 0, 0, 0))
Arguments
x
Vector of quantiles.
f
Vector of probabilities.
para
Numeric vector containing the parameters of the distribution,
in the order
$\xi, \alpha, \beta, \gamma, \delta$.
Value
cdfwak gives the distribution function;
quawak gives the quantile function.
Details
The Wakeby distribution with
parameters $\xi$,
$\alpha$,
$\beta$,
$\gamma$ and
$\delta$
has quantile function
$$x(F)=\xi+{\alpha\over\beta}(1-(1-F)^\beta)-{\gamma\over\delta}(1-(1-F)^\delta).$$
The parameters are restricted as in Hosking and Wallis (1997, Appendix A.11):
either$\beta+\delta>0$or$\beta=\gamma=\delta=0$;
if$\alpha=0$then$\beta=0$;
if$\gamma=0$then$\delta=0$;
$\gamma\ge0$;
$\alpha+\gamma\ge0$.
The distribution has a lower bound at $\xi$ and,
if $\delta
References
Hosking, J. R. M. and Wallis, J. R. (1997).
Regional frequency analysis: an approach based on L-moments,
Cambridge University Press, Appendix A.11.
See Also
cdfgpa for the generalized Pareto distribution.
cdfexp for the exponential distribution.