pdfgld {lmomco}R Documentation

Probability Density Function of the Generalized Lambda Distribution

Description

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

f(x) = {[(kappa(F)^{kappa-1} + h(F)^{h-1})*α]}^-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 speed increase because of the repeated calls to quagld.

Value

Probability density (f) for x.

Author(s)

W.H. Asquith

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))

[Package lmomco version 0.96.3 Index]