This paper derives a procedure for determining the expectations of order statistics associated with the standard normal distribution Z and its powers of order three and five (Z3 and Z5). the procedure is demonstrated for sample sizes of n ≤ 9. It is shown that Z3 and Z5 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 ≤ 5. For sample sizes of n = 6,7 the expectations of the order statistics for Z, Z3, and Z5 only require a single remainder term.
Headrick, Todd C. and Pant, Mohan D. "On the Order Statistics of Standard Normal-Based Power Method Distributions." (Jan 2012).