dgenf.orig(x, mu=0, sigma=1, s1, s2, log = FALSE) pgenf.orig(q, mu=0, sigma=1, s1, s2, lower.tail = TRUE, log.p = FALSE) qgenf.orig(p, mu=0, sigma=1, s1, s2, lower.tail = TRUE, log.p = FALSE) rgenf.orig(n, mu=0, sigma=1, s1, s2) Hgenf.orig(x, mu=0, sigma=1, s1, s2) hgenf.orig(x, mu=0, sigma=1, s1, s2)
length(n) > 1
, the length is
taken to be the number required.dgenf.orig
gives the density, pgenf.orig
gives the distribution
function, qgenf.orig
gives the quantile function, rgenf.orig
generates random deviates, Hgenf.orig
retuns the cumulative hazard
and hgenf.orig
the hazard.
$$f(x | \mu, \sigma, s_1, s_2) =
\frac{(s_1/s_2)^{s_1} e^{s_1 w}}{\sigma x (1 + s_1 e^w/s_2) ^ {(s_1 +
s_2)} B(s_1, s_2)}
$$
where $w = (log(x) - mu)/sigma$ ,
$B(s1,s2) = \Gamma(s1)\Gamma(s2)/\Gamma(s1+s2)$ is the beta function.
As $s2 -> infinity$, the distribution of
$x$ tends towards an original generalized gamma distribution with
the following parameters:
dgengamma.orig(x, shape=1/sigma, scale=exp(mu) / s1^sigma, k=s1)
See GenGamma.orig
for how this includes several other
common distributions as special cases.
The alternative parameterisation of the generalized F distribution,
originating from Prentice (1975) and given in this package as
GenF
, is
preferred for statistical modelling, since it is more stable as
$s1$ tends to infinity, and includes a further new class
of distributions with negative first shape parameter. The original
is provided here for the sake of completion and compatibility.
GenF
, GenGamma.orig
, GenGamma