ggammaUC {VGAM}R Documentation

The Generalized Gamma Distribution

Description

Density, distribution function, quantile function and random generation for the generalized gamma distribution with scale parameter scale, and parameters d and k.

Usage

dggamma(x, scale=1, d=1, k=1)
pggamma(q, scale=1, d=1, k=1)
qggamma(p, scale=1, d=1, k=1)
rggamma(n, scale=1, d=1, k=1)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations. Positive integer of length 1.
scale the (positive) scale parameter b.
d, k the (positive) parameters d and k.

Details

See ggamma, the VGAM family function for estimating the generalized gamma distribution by maximum likelihood estimation, for formulae and other details. Apart from n, all the above arguments may be vectors and are recyled to the appropriate length if necessary.

Value

dggamma gives the density, pggamma gives the distribution function, qggamma gives the quantile function, and rggamma generates random deviates.

Author(s)

T. W. Yee

References

Stacy, E. W. and Mihram, G. A. (1965) Parameter estimation for a generalized gamma distribution. Technometrics, 7, 349–358.

See Also

ggamma.

Examples

## Not run: 
x=seq(0, 14, by=0.01); d=1.5; Scale=2; k=6
plot(x, dggamma(x, Scale, d, k), type="l", col="blue", ylim=c(0,1),
     main="Blue is density, red is cumulative distribution function",
     sub="Purple are 5,10,...,95 percentiles", las=1, ylab="")
abline(h=0, col="blue", lty=2)
lines(qggamma(seq(0.05,0.95,by=0.05), Scale, d, k), 
      dggamma(qggamma(seq(0.05,0.95,by=0.05), Scale, d, k), Scale, d, k),
      col="purple", lty=3, type="h")
lines(x, pggamma(x, Scale, d, k), type="l", col="red")
abline(h=0, lty=2)
## End(Not run)

[Package VGAM version 0.7-7 Index]