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Results tagged with wishart-distribution
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user 795
The Wishart distribution is a common matrix distribution on square symmetric semi-definite matrices.
4
votes
2
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776
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What is the distribution of norm induced by an inverse Wishart?
Suppose $S$ is distributed as a Wishart matrix with $n$ degrees of freedom and scale matrix $\Sigma$, and let $\vec{a}$ be a fixed vector. It is well known that $\vec{a}^{\top}S\vec{a}$ is equal to
$ …
- 15k
4
votes
1
answer
312
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How do you translate a density from Cholesky factor to density of the matrix?
Suppose $L$ is a random $p\times p$ lower triangular matrix, with known density, $f(L)$. To compute the density of $C=L L^{\top}$, one needs to use the change of density formula. This is a little bit …
- 15k
3
votes
0
answers
417
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Distribution of a normalized inverse Wishart times Gaussian
Suppose $z\sim\mathcal{N}\left(\lambda^2 e_1,I_n\right)$ where $e_1$ is the first column of the $n$-dimensional identity matrix, denoted here as $I_n$. Suppose $S\sim\mathcal{W}\left(m,I_n\right)$ is …
- 15k
25
votes
1
answer
988
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Distribution of inverse Wishart to a power?
In a related question, I had asked about the norm induced by an inverse Wishart matrix. I am interested in generalizing that result somewhat. Let $A\sim\mathcal{W}_p\left(I,n\right)$, a Wishart matrix …
- 15k