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

Authors

Todd C. Headrick, Southern Illinois University CarbondaleFollow
Mohan Dev Pant, Southern Illinois University CarbondaleFollow

Comments

Published in ISRN Applied Mathematics, Vol. 2012, Article ID 945627 at doi:10.5402/2012/945627

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.

Recommended Citation

Headrick, Todd C. and Pant, Mohan D. "On the Order Statistics of Standard Normal-Based Power Method Distributions." (Jan 2012).