lmomco (version 2.4.14)

quagld: Quantile Function of the Generalized Lambda Distribution

Description

This function computes the quantiles of the Generalized Lambda distribution given parameters (\(\xi\), \(\alpha\), \(\kappa\), and \(h\)) of the distribution computed by pargld. The quantile function is $$x(F) = \xi + \alpha(F^{\kappa} - (1-F)^{h}) \mbox{,}$$ where \(x(F)\) is the quantile for nonexceedance probability \(F\), \(\xi\) is a location parameter, \(\alpha\) is a scale parameter, and \(\kappa\), and \(h\) are shape parameters. Note that in this parameterization, the scale term is shown in the numerator and not the denominator. This is done for lmomco as part of the parallel nature between distributions whose various scale parameters are shown having the same units as the location parameter.

Usage

quagld(f, para, paracheck=TRUE)

Value

Quantile value for nonexceedance probability \(F\).

Arguments

f

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

para

The parameters from pargld 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 quantile function in the context of TL-moments with nonzero trimming.

Author

W.H. Asquith

References

Asquith, W.H., 2007, L-moments and TL-moments of the generalized lambda distribution: Computational Statistics and Data Analysis, v. 51, no. 9, pp. 4484--4496.

Karian, Z.A., and Dudewicz, E.J., 2000, Fitting statistical distributions---The generalized lambda distribution and generalized bootstrap methods: CRC Press, Boca Raton, FL, 438 p.

See Also

cdfgld, pargld, lmomgld, lmomTLgld, pargld, parTLgld

Examples

if (FALSE) {
  para <- vec2par(c(123,34,4,3),type="gld")
  quagld(0.5,para, paracheck=FALSE)
}