Arcsine distribution
= Arcsine distribution
{title2=$\operatorname{Beta}(\tfrac12,\tfrac12)$}
{wiki}
The standard arcsine law has <probability density function> $1/[\pi\sqrt{x(1-x)}]$ on $(0,1)$. Substituting $x=\sin^2v$ in its integral gives <cumulative distribution function> $F(x)=2\arcsin\sqrt{x}/\pi$. Hence <inverse transform sampling> uses $X=\sin^2(\pi U/2)$ for $U$ with a continuous <uniform distribution>. The law places most of its density near the two endpoints rather than the middle.