lmomco (version 1.7.3)

quaglo: Quantile Function of the Generalized Logistic Distribution

Description

This function computes the quantiles of the Generalized Logistic distribution given parameters ($\xi$, $\alpha$, and $\kappa$) of the distribution computed by parglo. The quantile function of the distribution is

$$x(F) = \xi + \frac{\alpha}{\kappa}\left(1-\left(\frac{1-F}{F}\right)^\kappa\right) \mbox{ for } \kappa \ne 0 \mbox{ and}$$

$$x(F) = \xi - \alpha\log{\left(\frac{1-F}{F}\right)} \mbox{ for } \kappa = 0 \mbox{,}$$

where $x(F)$ is the quantile for nonexceedance probability $F$, $\xi$ is a location parameter, $\alpha$ is a scale parameter, and $\kappa$ is a shape parameter.

Usage

quaglo(f, para, paracheck=TRUE)

Arguments

f

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

para

The parameters from parglo 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 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.

See Also

cdfglo, parglo

Examples

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