lmomco (version 2.4.14)

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 \(h\)) computed by pargld or similar. The probability density function is $$f(x) = {[(\kappa[F(x)^{\kappa-1}] + h[1-F(x)])^{h-1})\times\alpha]}^{-1} \mbox{,}$$ where \(f(x)\) is the probability density function at \(x\), \(F(x)\) is the cumulative distribution function at \(x\).

Usage

pdfgld(x, para, paracheck)

Value

Probability density (\(f\)) for \(x\).

Arguments

x

A real value vector.

para

The parameters from pargld or vec2par.

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.

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, quagld, lmomgld, pargld

Examples

if (FALSE) {
# 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))
}