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lmgamma

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(y, p) = pi^(p * (p-1)/4) prod(gamma(y + (1-(1:p))/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)

Boom

Bayesian Object Oriented Modeling

v0.9.7
LGPL-2.1 | file LICENSE
Authors
Steven L. Scott is the sole author and creator of the BOOM project. Some code in the BOOM libraries has been modified from other open source projects. These include Cephes (obtained from Netlib, written by Stephen L. Moshier), NEWUOA (M.J.D Powell, obtained from Powell's web site), and a modified version of the R math libraries (R core development team). Original copyright notices have been maintained in all source files. In these cases, copyright claimed by Steven L. Scott is limited to modifications made to the original code. Google claims copyright for code written while Steven L. Scott was employed at Google from 2008 - 2018, but BOOM is not an officially supported Google project.
Initial release
2021-02-15

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