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Density, distribution function, quantile function and random
generation for the generalized gamma distribution with
scale parameter scale
,
and parameters d
and k
.
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)
vector of quantiles.
vector of probabilities.
number of observations.
Same as in runif
.
the (positive) scale parameter
the (positive) parameters
Logical.
If log = TRUE
then the logarithm of the density is returned.
dgengamma.stacy
gives the density,
pgengamma.stacy
gives the distribution function,
qgengamma.stacy
gives the quantile function, and
rgengamma.stacy
generates random deviates.
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.
Stacy, E. W. and Mihram, G. A. (1965) Parameter estimation for a generalized gamma distribution. Technometrics, 7, 349--358.
# 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)
# }
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