lmomco (version 1.4.3)

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 vec2par. The quantile function of the distribution 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 in this package as part of the parallel nature between distributions. The scale parameter is often shown have same units and the location parameter.

Usage

quagld(f, gldpara, paracheck=TRUE)

Arguments

f

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

gldpara

The parameters from vec2par 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

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

para <- vec2par(c(123,34,4,3),type="gld")
  quagld(0.5,para)