A special mathematical function related to the gamma function, generalized for multivariate distributions. The multivariate digamma function is the derivative of the log of the multivariate gamma function; for \(p = 1\) it is the same as the univariate digamma function.
$$\psi_{p}(a)=\sum _{i=1}^{p}\psi(a+(1-i)/2) $$ where \(\psi\) is the univariate digamma function (the derivative of the log-gamma function).
mvdigamma(x, p)
| x | non-negative numeric vector, matrix, or array |
|---|---|
| p | positive integer, dimension of a square matrix |
vector of values of multivariate digamma function.
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
digamma(1:10) #> [1] -0.5772157 0.4227843 0.9227843 1.2561177 1.5061177 1.7061177 #> [7] 1.8727843 2.0156415 2.1406415 2.2517526 mvdigamma(1:10, 1L) #> [1] -0.5772157 0.4227843 0.9227843 1.2561177 1.5061177 1.7061177 #> [7] 1.8727843 2.0156415 2.1406415 2.2517526