Some probabilistic properties of the generalized omega-square statistic

One considers the properties of the statistic $\Omega_n^2=(\mathbb Y_n-a)^T\mathbb C(\mathbb Y-a)$, where $\mathbb Y_n$ is the vector of the order statistics, constructed with respect to a sample of size $n$ from a uniform distribution on the segment $[0;1]$, $\mathbb C$ is a positive definite matrix of order $n$, and $a$ is an $n$-dimensional vector.