shapelog and ratelog.
dlgamma(x, shapelog, ratelog, log = FALSE)
plgamma(q, shapelog, ratelog, lower.tail = TRUE, log.p = FALSE)
qlgamma(p, shapelog, ratelog, lower.tail = TRUE, log.p = FALSE)
rlgamma(n, shapelog, ratelog)
mlgamma(order, shapelog, ratelog)
levlgamma(limit, shapelog, ratelog, order = 1)length(n) > 1, the length is
taken to be the number required.TRUE, probabilities/densities
$p$ are returned as $log(p)$.TRUE (default), probabilities are
$P[X <= x]$,="" otherwise,="" $p[x=""> x]$.dlgamma gives the density,
plgamma gives the distribution function,
qlgamma gives the quantile function,
rlgamma generates random deviates,
mlgamma gives the $k$th raw moment, and
levlgamma gives the $k$th moment of the limited loss
variable.Invalid arguments will result in return value NaN, with a warning.
shapelog $= a$ and ratelog $= b$ has density:
$$f(x) = \frac{\lambda^\alpha}{\Gamma(\alpha)}%
\frac{(\log x)^{\alpha - 1}}{x^{\lambda + 1}}$$
for $x > 1$, $a > 0$ and $b >
0$.
(Here $Gamma(a)$ is the function implemented
by R's gamma() and defined in its help.)The Loggamma is the distribution of the random variable $exp(X)$, where $X$ has a Gamma distribution with shape parameter $a$ and scale parameter $1/b$.
The $k$th raw moment of the random variable $X$ is $E[X^k]$ and the $k$th limited moment at some limit $d$ is $E[min(X, d)^k]$.
exp(dlgamma(2, 3, 4, log = TRUE))
p <- (1:10)/10
plgamma(qlgamma(p, 2, 3), 2, 3)
mlgamma(2, 3, 4) - mlgamma(1, 3, 4)^2
levlgamma(10, 3, 4, order = 2)
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