lmgamma {Boom}

Log Multivariate Gamma Function

Description

Returns the log of the multivariate gamma function.

Usage

lmgamma(y, dimension)

Arguments

y

The function argument, which must be a positive scalar.

dimension

The dimension of the multivariate gamma function, which must be an integer >= 1.

Details

The multivariate gamma function is

\Gamma_p(y) = \pi^{p(p-1)/4} \prod_{j =1}^p \Gamma(y + (1-j)/2).

The multivariate gamma function shows up as part of the normalizing constant for the Wishart and inverse Wishart distributions.

Value

Returns the log of the multivariate gamma function. Note that this function is not vectorized. Both y and dimension must be scalars, and the return value is a scalar.

Author(s)

Steven L. Scott [e-mail]