Probability content of a nearest neighbour ball
= Probability content of a nearest neighbour ball
{title2=$p_x(\rho_{(k)}(x))$}
For <independent and identically distributed random variables> with continuous distance <distribution function> $p_x$, the <probability integral transform> makes the probability content of the order-$k$ nearest ball a <uniform order statistic>, with the <Beta distribution> $\operatorname{Beta}(k,n+1-k)$.