quaglo: Quantile Function of the Generalized Logistic Distribution

Description

This function computes the quantiles of the Generalized Logistic distribution given parameters ($\xi$, $\alpha$, and $\kappa$) computed by parglo. The quantile function is $$x(F) = \xi + \frac{\alpha}{\kappa}\left(1-\left(\frac{1-F}{F}\right)^\kappa\right)\mbox{,}$$ for $\kappa \ne 0$, and $$x(F) = \xi - \alpha\log{\left(\frac{1-F}{F}\right)}\mbox{,}$$ for $\kappa = 0$, 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)

Value

Quantile value for for nonexceedance probability $F$.

Arguments

f: Nonexceedance probability ($0 \le F \le 1$).
para: The parameters from parglo or vec2par.
paracheck: A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.

Author

W.H. Asquith

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, v. 52, pp. 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 <- lmoms(c(123,34,4,654,37,78))
  quaglo(0.5,parglo(lmr))

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