Beta, Dirichlet, and von Mises-Fisher
Chapter 13: Probability and Random Variables — Beta,Dirichlet,vMF
From the book
Chapter 13: Probability and Random Variables. In the chapter mind map this icon labels Beta,Dirichlet,vMF. The discussion below is excerpted and lightly edited from § Definition: Beta Distribution in Mathematics for AI and Machine Learning.
A random variable $X$ follows a Beta distribution with shape parameters $\alpha > 0$ and $\beta > 0$, denoted as $X \sim \mathrm{Beta}(\alpha, \beta)$, if its probability density function is:
where $\Gamma(\cdot)$ is the gamma function. The normalization constant $\frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)}$ ensures that the PDF integrates to 1 over $[0, 1]$.
What this drawing shows
What you see. Groups common distribution families for simplex, probability, and directional data: Beta, Dirichlet, and vMF.
In the mind map. Chapter 13 — Beta,Dirichlet,vMF. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 13: Probability and Random Variables — see the mind-map node Beta,Dirichlet,vMF.