On the Order Statistics of Standard Normal-Based Power Method Distributions. (20th May 2012) - Headrick, Todd C.; Pant, Mohan D.
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 (Z 3 and Z 5 ). The procedure is demonstrated for sample sizes of n ≤ 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 ≤ 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.