Matrix gamma distribution
Notation | |||
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Parameters | shape parameter (real) | ||
Support | positive-definite real matrix | ||
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In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices.[1] It is effectively a different parametrization of the Wishart distribution, and is used similarly, e.g. as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal distribution. The compound distribution resulting from compounding a matrix normal with a matrix gamma prior over the precision matrix is a generalized matrix t-distribution.[1]
A matrix gamma distributions is identical to a Wishart distribution with
Notice that the parameters and are not identified; the density depends on these two parameters through the product .
See also
- inverse matrix gamma distribution.
- matrix normal distribution.
- matrix t-distribution.
- Wishart distribution.
Notes
- ^ a b Iranmanesh, Anis, M. Arashib and S. M. M. Tabatabaey (2010). "On Conditional Applications of Matrix Variate Normal Distribution". Iranian Journal of Mathematical Sciences and Informatics, 5:2, pp. 33–43.
References
- Gupta, A. K.; Nagar, D. K. (1999) Matrix Variate Distributions, Chapman and Hall/CRC ISBN 978-1584880462
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univariate
with finite support | |
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with infinite support |
univariate
univariate
continuous- discrete |
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(joint)
- Discrete:
- Ewens
- multinomial
- Continuous:
- Dirichlet
- multivariate Laplace
- multivariate normal
- multivariate stable
- multivariate t
- normal-gamma
- Matrix-valued:
- LKJ
- matrix normal
- matrix t
- matrix gamma
- Wishart
- Univariate (circular) directional
- Circular uniform
- univariate von Mises
- wrapped normal
- wrapped Cauchy
- wrapped exponential
- wrapped asymmetric Laplace
- wrapped Lévy
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- Kent
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- bivariate von Mises
- Multivariate
- von Mises–Fisher
- Bingham
and singular
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- Dirac delta function
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- Cantor
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