Generalized Gamma Distribution

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.

Value

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

References

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

Author

T. W. Yee and Kai Huang

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.

Examples

if (FALSE)  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 the CDF",
     sub = "Purple are 5,10,...,95 percentiles", las = 1, ylab = "")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
abline(h = 0, col = "blue", lty = 2)
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet
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")
#> Error in plot.xy(xy.coords(x, y), type = type, ...): plot.new has not been called yet
lines(x, pgengamma.stacy(x, Scale, d = d, k = k), col = "orange")
#> Error: object 'x' not found
abline(h = 0, lty = 2)  # \dontrun{}
#> Error in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): plot.new has not been called yet