quawak: Quantile Function of the Wakeby Distribution

Description

This function computes the quantiles of the Wakeby distribution given parameters ($\xi$, $\alpha$, $\beta$, $\gamma$, and $\delta$) of the distribution computed by parwak. The quantile function of the distribution is

$$x(F) = \xi+\frac{\alpha}{\beta}(1-(1-F)^\beta)- \frac{\gamma}{\delta}(1-(1-F))^{-\delta} \mbox{,}$$

where $x(F)$ is the quantile for nonexceedance probability $F$, $\xi$ is a location parameter, $\alpha$ and $\beta$ are scale parameters, and $\gamma$, and $\delta$ are shape parameters. The five returned parameters from parwak in order are $\xi$, $\alpha$, $\beta$, $\gamma$, and $\delta$.

Usage

quawak(f, wakpara, paracheck=TRUE)

Arguments

Nonexceedance probability ($0 \le F \le 1$).

wakpara

The parameters from parwak or similar.

paracheck

A logical controlling whether the parameters and checked for validity. Overriding of this check might be extremely important and needed for use of the distribution quantile function in the context of TL-moments with nonzero trimming.

Value

Quantile value for nonexceedance probability $F$.

References

Hosking, J.R.M., 1990, L-moments---Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105--124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

Examples

Run this code

lmr <- lmom.ub(c(123,34,4,654,37,78))
  quawak(0.5,parwak(lmr))