quagam: Quantile Function of the Gamma Distribution

Description

This function computes the quantiles of the Gamma distribution given parameters ($\alpha$ and $\beta$) of the distribution computed by pargam. The quantile function has no explicit form. See the qgamma function and cdfgam. The parameters have the following interpretations: $\alpha$ is a shape parameter and $\beta$ is a scale parameter in the R syntax.

Usage

quagam(f, para, paracheck=TRUE)

Arguments

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

para

The parameters from pargam 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))
  g <- pargam(lmr)
  quagam(0.5,g)
 
  # generate 50 random samples from this fitted parent
  Qsim <- rlmomco(5000,g)
  # compute the apparent gamma parameter for this parent
  gsim <- pargam(lmoms(Qsim))