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In statistics, the inverse Dirichlet distribution is a derivation of the matrix variate Dirichlet distribution. It is related to the inverse Wishart distribution.
Suppose
are
positive definite matrices with a matrix variate Dirichlet distribution,
. Then
have an inverse Dirichlet distribution, written
. Their joint probability density function is given by
![{\displaystyle \left\{\beta _{p}\left(a_{1},\ldots ,a_{r};a_{r+1}\right)\right\}^{-1}\prod _{i=1}^{r}\det \left(X_{i}\right)^{-a_{i}-(p+1)/2}\det \left(I_{p}-\sum _{i=1}^{r}{X_{i}}^{-1}\right)^{a_{r+1}-(p+1)/2}}](https://wikimedia.riteme.site/api/rest_v1/media/math/render/svg/af957d93d8a5a93a5752667c64c1947b0d5f2d37)
References[edit]
A. K. Gupta and D. K. Nagar 1999. "Matrix variate distributions". Chapman and Hall.
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Discrete univariate | with finite support | |
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with infinite support | |
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Continuous univariate | supported on a bounded interval | |
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supported on a semi-infinite interval | |
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supported on the whole real line | |
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with support whose type varies | |
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Mixed univariate | |
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Multivariate (joint) | |
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Directional | |
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Degenerate and singular | |
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Families | |
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