Beta Distribution

Gist

A pretty versatile probability distribution that is useful in cases where there is random variables bound to intervals between 0 and 1. Use for percentages and proportions.

Mathematics

A continuous probability distribution.

where B is equal to $\frac{\mathrm{\Gamma }(\alpha +\beta )}{\mathrm{\Gamma }(\alpha )\mathrm{\Gamma }(\beta )}$ and serve as a normalizing function.

Properties

Must be true: $\alpha >0$ and $\beta >0$
Mean: $\frac{\alpha }{\alpha +\beta }$
Variance: $\frac{\alpha \beta }{(\alpha +\beta {)}^2\alpha +\beta +1}$

Relationship

1. Is the Conjugate Prior for a binomial posterior distribution

Uses

References

1. https://www.robertkubinec.com/post/limited_dvs/
2. https://www.robertkubinec.com/post/nasa_beta/