I have a $d$-dimensional ($d>3$) array (vector, set, ...) which is filled with random values taken from uniform distribution (interval $[0,1]$). What is the probability distribution for n-th smallest array component?
I am already aware that first smallest (the smallest) value, $r_1$, has the following distribution:
$P(r_1 < y ) = y^d .$
While the $d$-th smallest (the largest) value, $r_d$, has the following distribution:
$P(r_d < y) = 1 - (1-y)^d .$
But how do I obtain distributions of intermediate values?