ChisqSupp {actuar} R Documentation

## 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(t, 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). `t` 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)] and the moment generating function is E[e^{tX}].

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`).

### Value

`mchisq` gives the kth raw moment, `levchisq` gives the kth moment of the limited loss variable, and `mgfchisq` gives the moment generating function in `t`.

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

### Author(s)

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

### References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.

Johnson, N. L. and Kotz, S. (1970), Continuous Univariate Distributions, Volume 1, Wiley.

`Chisquare`
```mchisq(2, 3, 4)