gbd function

Basic functions for RS-GLD

To compute the density, distribution, quantile, and to generate random sample for RS-GLD.

## Default S3 method:
degld(x,lambda)
pegld(x,lambda)
qegld(p,lambda)
regld(n,lambda)

Arguments

• x: a numeric value or a vector.
• p: a probability or a vector of probabilities.
• n: sample size.
• lambda: a vector of four parameters for RS-GLD.

Author(s)

B. Wang bwang@jaguar1.usouthal.edu

References

Karian, Z.A., Dudewicz, E.J., McDonald, P., 1996. The Extended Generalized Lambda Distribution System for Fitting Distributions to Data: history,completion of theory, tables, applications, the ``final word'' on moment fits, Comm. in Statist.- Simul. & Comput.

25 (3), 611-642.

Karian, Z.A., Dudewicz, E.J., 2000. Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods, Chapman and Hall/CRC.

See Also

fit.egld, qrsgld,prsgld, rrsgld,drsgld.

Examples

lambdas = c(2,4,3,4)
shape=3;scale=4
x0 = rbeta(5,shape,scale)
x1 = x0*lambdas[2]+lambdas[1]
qegld(c(0,.1,.5,.7,1),lambdas)
qbeta(c(0,.1,.5,.7,1),shape,scale)*lambdas[2]+lambdas[1]

pegld(x1,lambdas)
pbeta(x0,shape,scale)

degld(x1,lambdas)
dbeta(x0,shape,scale)/lambdas[2]

x0 = sort(rbeta(1000,shape,scale))
y = x0*lambdas[2]+lambdas[1]
plot(dbeta(x0,shape,scale)/lambdas[2]~y,type='l')
lines(degld(y,lambdas)~y,lty=2,col=2)
lines(density(y),col=4,lty=3)