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mvdigamma: Multivariate Digamma Function

Description

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).

Usage

mvdigamma(x, p)

Value

vector of values of multivariate digamma function.

Arguments

x

non-negative numeric vector, matrix, or array

p

positive integer, dimension of a square matrix

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, lgamma, digamma, and mvgamma

Examples

Run this code
digamma(1:10)
mvdigamma(1:10, 1L)

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