InverseGamma {actuar}

[size=1.4em]The Inverse Gamma Distribution


Package:
actuar


Version:
1.1-6



Description

Density function, distribution function, quantile function, random generation, raw moments, and limited moments for the Inverse Gamma distribution with parameters shape and scale.

Usagedinvgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)pinvgamma(q, shape, rate = 1, scale = 1/rate,          lower.tail = TRUE, log.p = FALSE)qinvgamma(p, shape, rate = 1, scale = 1/rate,          lower.tail = TRUE, log.p = FALSE)rinvgamma(n, shape, rate = 1, scale = 1/rate)minvgamma(order, shape, rate = 1, scale = 1/rate)levinvgamma(limit, shape, rate = 1, scale = 1/rate,            order = 1)mgfinvgamma(x, shape, rate =1, scale = 1/rate, log =FALSE)
Argumentsx, qvector of quantiles.pvector of probabilities.nnumber of observations. If length(n) > 1, the length is taken to be the number required.shape, scaleparameters. Must be strictly positive.ratean alternative way to specify the scale.log, log.plogical; if TRUE, probabilities/densities p are returned as log(p).lower.taillogical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].orderorder of the moment.limitlimit of the loss variable.
Details

The Inverse Gamma distribution with parameters shape = a and scale = s has density: for x > 0, a > 0 and s > 0. (Here Gamma(a) is the function implemented by R's gamma() and defined in its help.)

The special case shape == 1 is an Inverse Exponential distribution.

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].

The moment generating function is given by E[e^{xX}].

Values

dinvgamma gives the density, pinvgamma gives the distribution function, qinvgamma gives the quantile function, rinvgamma generates random deviates, minvgamma gives the kth raw moment, and levinvgammagives the kth moment of the limited loss variable, mgfinvgamma gives the moment generating function in x.

Invalid arguments will result in return value NaN, with a warning.

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2008), Loss Models, From Data to Decisions, Third Edition, Wiley.

Note

Also known as the Vinci distribution.

Examples
exp(dinvgamma(2, 3, 4, log = TRUE))p <- (1:10)/10pinvgamma(qinvgamma(p, 2, 3), 2, 3)minvgamma(-1, 2, 2) ^ 2levinvgamma(10, 2, 2, order = 1)mgfinvgamma(1,3,2)


Author(s)

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

Documentation reproduced from package actuar, version 1.1-6. License: GPL (>= 2)

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