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.
Citation
Howard L. Jones. "Exact Lower Moments of Order Statistics in Small Samples from a Normal Distribution." Ann. Math. Statist. 19 (2) 270 - 273, June, 1948. https://doi.org/10.1214/aoms/1177730253
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