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Add relations for the Student t distributions #62

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rlouf opened this issue Sep 24, 2022 · 0 comments
Open

Add relations for the Student t distributions #62

rlouf opened this issue Sep 24, 2022 · 0 comments
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enhancement New feature or request help wanted Extra attention is needed mathematical relations

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@rlouf
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rlouf commented Sep 24, 2022

  1. If $Z \sim \operatorname{Norm}(0,1)$ and $\chi^2 \sim \operatorname{ChiSquared}(n)$ then $Y = \frac{Z}{\sqrt{\chi^2 /n}} \sim \operatorname{T}(n)$. Falls under Add ratio distributions relations #65.
  2. If $X \sim \operatorname{Norm}(\mu, \sigma)$, $\tau = 1 / \sigma^2 \sim \operatorname{Gamma}(\alpha, \beta)$ then $X$ is a random variable with a Student's t distribution. This one falls under Add more scale-mixtures #49.
@rlouf rlouf added help wanted Extra attention is needed mathematical relations enhancement New feature or request labels Sep 24, 2022
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Labels
enhancement New feature or request help wanted Extra attention is needed mathematical relations
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