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Home > Multivariate gamma function

It has two equivalent definitions:

where is the set of all positive-definite matrices. The other is more useful in practice:

Thus

and so on.

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Topics: Multivariate Gamma Function Statistics Equivalent...

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Multivariate statisticsMultivariate statistics or multivariate statistical analysis in statistics describes a collection of procedures which involve observation and analysis of more than one statistical variable at a time. There are many different models, each with its own type Multivariate random variableA multivariate random variable or random vector is a vector X X . X whose components are scalar-valued random variables on the same probability space (Ω, P). Every such random vector gives rise to a probability measure on R n with the Borel algebra Multivariate normal distributionIn probability theory and statistics, a random vector X X . X follows a multivariate normal distribution also sometimes called a multivariate Gaussian distribution (in honor of Carl Friedrich Gauss, who was not the first to write about the normal distribu Multivariate calculusMultivariate calculus is a means of analyzing deterministic systems with multiple degrees of freedom. Functions with independent variables corresponding to each of the degrees of freedom are often used to model these systems, and the calculus provides too Multivariate division algorithmAlthough polynomials in more than one variable do not form a Euclidean domain, so it is not possible to construct a true division algorithm, an approximate multivariate division algorithm can be constructed. Given a polynomial g polynomials f . f and an o Multivariate gamma functionIn mathematics, the multivariate gamma distribution , , is a generalization of the gamma function. It is useful in multivariate statistics. It has two equivalent definitions: : where is the set of all positive-definite matrices. The other is more useful i