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)

Arguments

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

wakpara

The parameters from parwak or similar.

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))