Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 945627, 13 pages
http://dx.doi.org/10.5402/2012/945627
Research Article

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

Section on Statistics and Measurement, Department of EPSE, Southern Illinois University Carbondale, P.O. Box 4618, 222-J Wham Building, Carbondale, IL 62901-4618, USA

Received 17 January 2012; Accepted 5 March 2012

Academic Editors: T. Y. Kam and G. Stavroulakis

Copyright © 2012 Todd C. Headrick and Mohan D. Pant. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.