Loggamma {actuar} | 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
= 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], k < ratelog.
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)