On the Order Statistics of Standard Normal-Based Power Method Distributions. (20th May 2012)

• Record Type: Journal Article
• Authors: Headrick, Todd C.; Pant, Mohan D.
• Other Names: Kam T. Y. Academic Editor.; Stavroulakis G. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2012(2012)
• Publication Date: 2012-05-20
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.5402/2012/945627
• Languages: English
• ISSNs: 2090-5564

Abstract

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.