Loggamma {actuar}R Documentation

The Loggamma Distribution

Description

Density function, distribution function, quantile function, random generation, raw moments and limited moments for the Loggamma distribution with parameters shapelog and ratelog.

Usage

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)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n 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).
lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
order order of the moment.
limit limit of the loss variable.

Details

The Loggamma distribution with parameters shapelog = a and ratelog = b has density:

f(x) = (b^a (log(x))^(a - 1))/(Gamma(a) * x^(b + 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 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].

Value

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.

Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon

References

Hogg, R. V. and Klugman, S. A. (1984), Loss Distributions, Wiley.

Examples

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)
[Package actuar version 1.0-2 Index]