actuar (version 1.2-2)

InvGaussSupp: 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.

Value

minvGauss gives the $k$th raw moment, levinvGauss gives the $k$th 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.

Details

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

The moment generating function is defined for x <= lambda="" (2="" *="" nu^2)<="" code="">.

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(0.2, 3, 4)