InvGaussSupp {actuar}R Documentation

Moments and Moment Generating Function of the Inverse Gaussian Distribution

Description

Raw moments, limited moments and moment generating function for the Inverse Gaussian distribution with parameters nu and lambda.

Usage

minvGauss(order, nu, lambda)
levinvGauss(limit, nu, lambda, order = 1)
mgfinvGauss(x, nu, lambda, log= FALSE)

minvgauss(order, nu, lambda)
levinvgauss(limit, nu, lambda, order = 1)
mgfinvgauss(x, nu, lambda, log= FALSE)

Arguments

order order of the moment. Only order = 1 is supported by levinvGauss.
limit limit of the loss variable.
nu, lambda parameters. Must be strictly positive.
x numeric vector.
log logical; if TRUE, the cumulant generating function is returned.

Details

The kth raw moment of the random variable X is E[X^k], the kth limited moment at some limit d is E[min(X, d)^k] and the moment generating function is E[e^{xX}].

Value

minvGauss gives the kth raw moment, levinvGauss gives the kth moment of the limited loss variable, and mgfinvGauss gives the moment generating function in x.
Invalid arguments will result in return value NaN, with a warning.

Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca, Christophe Dutang

References

Chhikara, R. S. and Folk, T. L. (1989), The Inverse Gaussian Distribution: Theory, Methodology and Applications, Decker.

Seshadri, D. N. (1989), The Inverse Gaussian Distribution: Statistical Theory and Applications, Springer.

See Also

invGauss in package SuppDists for the density function, distribution function, quantile function and random number generator.

Examples

minvGauss(2, 3, 4) 
levinvGauss(10, 3, 4)
mgfinvGauss(1,3,2)
[Package actuar version 1.0-2 Index]