Loggamma | R Documentation |
Density function, distribution function, quantile function, random generation,
raw moments and limited moments for the Loggamma distribution with
parameters 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)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
shapelog, ratelog |
parameters. Must be strictly positive. |
log, log.p |
logical; if |
lower.tail |
logical; if |
order |
order of the moment. |
limit |
limit of the loss variable. |
The loggamma distribution with parameters shapelog
=
\alpha
and ratelog
= \lambda
has density:
f(x) = \frac{\lambda^\alpha}{\Gamma(\alpha)}%
\frac{(\log x)^{\alpha - 1}}{x^{\lambda + 1}}
for x > 1
, \alpha > 0
and \lambda > 0
.
(Here \Gamma(\alpha)
is the function implemented
by R's gamma()
and defined in its help.)
The loggamma is the distribution of the random variable
e^X
, where X
has a gamma distribution with
shape parameter alpha
and scale parameter
1/\lambda
.
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]
, k < \lambda
.
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.
The "distributions"
package vignette provides the
interrelations between the continuous size distributions in
actuar and the complete formulas underlying the above functions.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Hogg, R. V. and Klugman, S. A. (1984), Loss Distributions, Wiley.
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)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.