On the order statistics of standard normal-based power method distributions (Q1954431)

Summary: We derive a procedure for determining the expectations of order statistics associated with the standard normal distribution (\(Z\)) and its powers of order three and five (\(Z^3\) and \(Z^5\)). The procedure is demonstrated for sample sizes of \(n \leq 9\). It is shown that \(Z^3\) and \(Z^5\) have expectations of order statistics that are functions of the expectations for \(Z\) and can be expressed in terms of explicit elementary functions for sample sizes of \(n \leq 5\). For sample sizes of \(n = 6, 7\) the expectations of the order statistics for \(Z\), \(Z^3\), and \(Z^5\) only require a single remainder term.