Gld {Davies}

The Generalized Lambda Distribution

Description

Density, distribution function, quantile function and random generation for the Generalized Lambda Distribution

Usage

dgld(x, params)
dgld.p(x, params)
pgld(q, params)
qgld(p, params)
rgld(n, params)

Arguments

x, q

vector of quantiles

p

vector of probabilities

n

In function rgld(), the number of observations. If length(n)> 1, the length is taken to be the number required

params

vector of parameters: params[1]==lambda1 et seq

Details

The Generalized Lambda distribution has quantile function

\[f(x)=\lambda_1 +(p^{\lambda_3} - (1-p)^{\lambda_4})/\lambda_2\]

Value

Function dgld() gives the density, dgld.p() gives the density in terms of the quantile, pgld() gives the distribution function, qgld() gives the quantile function, and rgld() generates random deviates.

References

• M. J. Wichura 1988. “Algorithm AS 241: The Percentage Points of the Normal Distribution”. Applied Statistics, 37, 477–484.

• A. Ozturk and R. F. Dale 1985. “Least squares estimation of the parameters of the generalized lambda distribution”. Technometrics 27(1):84

See Also

Davies, expected.gld

Examples

params <- c(4.114,0.1333,0.0193,0.1588)  #taken straight from some paper

gld.rv <- rgld(100,params)

hist(gld.rv)
fit.davies.q(gld.rv)  #remember the Davies distn has 3 DF and the GLD 4...