mgamma

Given a vector of points <code>x</code> and an order <code>p</code>, compute the multivariate gamma function. The function is defined as
$$\gamma_p(x) = \pi^{p(p-1)/4}\prod_{i=1}^p \Gamma\{x + (1-i)/2\}.$$

Kernel smoothing for Wishart random matrices described in Daayeb, Khardani and Ouimet (2025) <doi:10.48550/arXiv.2506.08816>, Gaussian and log-Gaussian models using least square or likelihood cross validation criteria for optimal bandwidth selection.

Leo Belzile

Kernel Density Estimation for Random Symmetric Positive Definite
Matrices

Frederic Ouimet

mgamma function

<dl><dt>x</dt>
<dd>[vector] of points at which to evaluate the function</dd>
<dt>p</dt>
<dd>[int] dimension of the multivariate gamma function, strictly positive.</dd>
<dt>log</dt>
<dd>[logical] if <code>TRUE</code>, returns the log multivariate gamma function.</dd></dl>

Arguments

Multivariate gamma function — mgamma

<dl>

<dt>x</dt>
<dd>[vector] of points at which to evaluate the function</dd>


<dt>p</dt>
<dd>[int] dimension of the multivariate gamma function, strictly positive.</dd>


<dt>log</dt>
<dd>[logical] if <code>TRUE</code>, returns the log multivariate gamma function.</dd>

</dl>

mgamma: Multivariate gamma function

Description

Usage

Value

Arguments