matrix gamma distribution
{{Short description|Generalization of gamma distribution}}
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name =Matrix gamma|
type =density|
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parameters = shape parameter (real)
scale (positive-definite real matrix)
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support = positive-definite real matrix|
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- is the multivariate gamma function.|
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In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices.Iranmanesh, Anis, M. Arashib and S. M. M. Tabatabaey (2010). [http://www.ijmsi.ir/browse.php?a_code=A-10-1-83&slc_lang=en&sid=1 "On Conditional Applications of Matrix Variate Normal Distribution"]. Iranian Journal of Mathematical Sciences and Informatics, 5:2, pp. 33–43. 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.
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
Notes
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References
- Gupta, A. K.; Nagar, D. K. (1999) Matrix Variate Distributions, Chapman and Hall/CRC {{ISBN|978-1584880462}}
{{ProbDistributions|multivariate}}
Category:Continuous distributions
Category:Multivariate continuous distributions
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