R: The Generalized Gamma Distribution

gengammaUC {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

    dgengamma.stacy(x, scale = 1, d, k, log = FALSE)
    pgengamma.stacy(q, scale = 1, d, k,
                    lower.tail = TRUE, log.p = FALSE)
    qgengamma.stacy(p, scale = 1, d, k,
                    lower.tail = TRUE, log.p = FALSE)
    rgengamma.stacy(n, scale = 1, d, k)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Same as in `runif`.
`scale` | the (positive) scale parameter b.
`d, k` | the (positive) parameters d and k. Both can be thought of as shape parameters, where d is of the Weibull-type and k is of the gamma-type.
`log` | Logical. If `log = TRUE` then the logarithm of the density is returned.
`lower.tail, log.p` | Same meaning as in `pnorm` or `qnorm`.

### Details

See `gengamma.stacy`, 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

`dgengamma.stacy` gives the density, `pgengamma.stacy` gives the distribution function, `qgengamma.stacy` gives the quantile function, and `rgengamma.stacy` generates random deviates.

### Author(s)

T. W. Yee and Kai Huang

### References

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

### See Also

`gengamma.stacy`.

### Examples

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

[Package VGAM version 1.1-3 Index]