Editing Beta distribution (section)

===Derived from other distributions===
* The ''k''th [[order statistic]] of a sample of size ''n'' from the [[Uniform distribution (continuous)|uniform distribution]] is a beta random variable, ''U''<sub>(''k'')</sub> ~ Beta(''k'', ''n''+1−''k'').<ref name=David1/>
* [[Gamma distribution]]: If ''X'' ~ Gamma(α, θ) and ''Y'' ~ Gamma(β, θ) are independent, then <math>\tfrac{X}{X+Y} \sim \operatorname{Beta}(\alpha, \beta)\,</math>.
* [[Chi-squared distribution]]: If <math>X \sim \chi^2(\alpha)\,</math> and <math>Y \sim \chi^2(\beta)\,</math> are independent, then <math>\tfrac{X}{X+Y} \sim \operatorname{Beta}(\tfrac{\alpha}{2}, \tfrac{\beta}{2})</math>.
* The [[Power transformation (statistics)|power transformation]] for the uniform distribution: If ''X'' ~ U(0, 1) and ''α'' > 0 then ''X''<sup>1/''α''</sup> ~ Beta(''α'', 1).
* [[Cauchy distribution]]: If ''X'' ~ Cauchy(0, 1) then <math>\tfrac{1}{1+X^2} \sim \operatorname{Beta}\left(\tfrac12, \tfrac12\right)\,</math>