actuar (version 0.9-4)

ChisqSupp: Moments and Moment Generating Function of the (non-central) Chi-Squared Distribution

Description

Raw moments, limited moments and moment generating function for the chi-squared ($\chi^2$) distribution with df degrees of freedom and optional non-centrality parameter ncp.

Usage

mchisq(order, df, ncp = 0)
levchisq(limit, df, ncp = 0, order = 1)
mgfchisq(x, df, ncp = 0, log= FALSE)

Arguments

order

order of the moment.

limit

limit of the loss variable.

df

degrees of freedom (non-negative, but can be non-integer).

ncp

non-centrality parameter (non-negative).

x

numeric vector.

log

logical; if TRUE, the cumulant generating function is returned.

Value

• mchisq gives the $k$th raw moment, levchisq gives the $k$th moment of the limited loss variable, and mgfchisq 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 $E[\min(X, d)]$ and the moment generating function is $E[e^{xX}]$.

Only integer moments are supported for the non central Chi-square distribution (ncp > 0). The limited expected value is supported for the centered Chi-square distribution (ncp = 0).

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley. Johnson, N. L. and Kotz, S. (1970), Continuous univariate distributions, Volume 1, Wiley.

See Also

Chisquare

Examples

mchisq(2, 3, 4)
levchisq(10, 3, order = 2)
mgfchisq(1, 3, 2)