lmvgamma {CholWishart}

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)=\pi^{p(p-1)/4}\prod_{j=1}^{p} \Gamma [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

See Also

gamma and lgamma

Examples

lgamma(1:12)
lmvgamma(1:12, 1L)
mvgamma(1:12, 1L)
gamma(1:12)