lmvgamma {CholWishart} R Documentation

## Multivariate Gamma Function

### Description

A special mathematical function related to the gamma function, generalized for multivariate gammas. `lmvgamma` is the log of the multivariate gamma, `mvgamma`.

The multivariate gamma function for a dimension p is defined as:

Gamma_p(a)=π^{p(p-1)/4}* Prod_{j=1}^{p}Γ[a+(1-j)/2]

For p = 1, this is the same as the usual gamma function.

### Usage

```lmvgamma(x, p)

mvgamma(x, p)
```

### Arguments

 `x` non-negative numeric vector, matrix, or array `p` positive integer, dimension of a square matrix

### Value

For `lmvgamma` log of multivariate gamma of dimension `p` for each entry of `x`. For non-log variant, use `mvgamma`.

### Functions

• `mvgamma`: Multivariate gamma function.

### References

A. K. Gupta and D. K. Nagar 1999. Matrix variate distributions. Chapman and Hall.

Multivariate gamma function. In Wikipedia, The Free Encyclopedia,from https://en.wikipedia.org/w/index.php?title=Multivariate_gamma_function&oldid=808084916

`gamma` and `lgamma`
```lgamma(1:12)