Beta sampling by uniform order statistics
= Beta sampling by uniform order statistics
For positive integers $\alpha,\beta$, the $\alpha$th <order statistic> from $\alpha+\beta-1$ independent <uniform distributions> on $(0,1)$ has <Beta distribution> $\operatorname{Beta}(\alpha,\beta)$. Selecting the observations below and above a value $u$ gives its <probability density function> proportional to $u^{\alpha-1}(1-u)^{\beta-1}$, with normalizing factor $(\alpha+\beta-1)!/((\alpha-1)!(\beta-1)!)$.