On the Order Statistics of Standard Normal-Based Power Method Distributions

Abstract EN

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.