Loggamma: The Loggamma Distribution

LoggammaR Documentation

The Loggamma Distribution


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.


vector of probabilities.


number of observations. If length(n) > 1, the length is taken to be the number required.

shapelog, ratelog

parameters. Must be strictly positive.

log, log.p

logical; if TRUE, probabilities/densities p are returned as \log(p).


logical; if TRUE (default), probabilities are P[X \le x], otherwise, P[X > x].


order of the moment.


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 kth raw moment of the random variable X is E[X^k] and the kth 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 kth raw moment, and levlgamma gives the kth 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)

actuar documentation built on Nov. 8, 2023, 9:06 a.m.