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, log=FALSE)
    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.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### 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 0.7-9 Index]