On the order statistics of standard normal based power method distributions
Abstract
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.