Exact Lower Moments of Order Statistics in Small Samples from a Normal Distribution

Abstract

Exact means in samples of size $\geq 3$, and exact second moments and product-moments in samples of size $\leq 4$, are given in Table 1 in terms of $\pi$ for order statistics selected from the normal distribution $N(0, 1)$. The derivation employs multiple integration and some general properties of the moments.