VGAM (version 0.7-5)

ggammaUC: 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 $k$.

Value

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

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.

References

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

See Also

ggamma.

Examples

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)