Distribution |
Notation |
Parameters |
Density function |
Moments, entropy, KL-divergence, etc. |
Notes |
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Uniform |
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Exponential |
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Laplace |
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mean |
decay scale |
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mean vector |
covariance |
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Gamma |
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shape ![$ \alpha>0$](img34.png) |
inv. scale |
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conj. Gaussian precision |
where |
then...
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Inverse gamma |
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Wishart |
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deg. of freedom |
precision matrix |
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Inverse-Wishart |
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deg. of freedom ![$ \nu$](img49.png) |
covariance matrix |
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entropy |
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conj. Gaussian covariance |
If
, then |
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Student-t (1) |
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deg. of freedom ![$ \nu>0$](img65.png) |
mean ; scale |
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Student-t (2) |
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(relative to Gaussian) |
equiv.
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deg. of freedom ![$ \nu>0$](img65.png) |
mean
;
matrix |
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Beta |
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prior sample sizes |
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Dirichlet |
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prior sample sizes |
![$ \boldsymbol{\alpha}= \{\alpha_1,\ldots,\alpha_k\}$](img93.png) |
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number and value
![$ \boldsymbol{\nu}$](img105.png) |
of pseudo-observations |
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