lmomco (version 1.7.3)

pdfgld: Probability Density Function of the Generalized Lambda Distribution

Description

This function computes the probability density function of the Generalized Lambda distribution given parameters ($\xi$, $\alpha$, $\kappa$, and $h$) of the distribution computed by pargld or similar. The probability density function is

$$f(x) = {[(\kappa(F^{\kappa-1}) + h(1-F)^{h-1})\times\alpha]}^{-1} \mbox{at\ } x = Q(F)$$

where $f(x)$ is the probability density function at $x$, $Q(F)$ is the quantile function for nonexceedance probability $F$.

Usage

pdfgld(x, gldpara, paracheck)

Arguments

x

A real value.

gldpara

The parameters from pargld or similar.

paracheck

A logical switch as to whether the validity of the parameters should be checked. Default is paracheck=TRUE. This switch is made so that the root solution needed for cdfgld exhibits an extreme sp

Value

• Probability density ($f$) for $x$.

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, quagld, lmomgld, pargld

Examples

# Using Karian and Dudewicz, 2000, p. 10
gld <- vec2par(c(0.0305,1/1.3673,0.004581,0.01020),type='gld')
quagld(0.25,gld) # which equals about 0.028013 as reported by K&D
pdfgld(0.028013,gld) # which equals about 43.04 as reported by K&D
F <- seq(.001,.999,by=.001)
x <- quagld(F,gld)
plot(x, pdfgld(x,gld), type='l', xlim=c(0,.1))