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On the Order Statistics of Standard Normal-Based Power Method Distributions
ISRN Applied Mathematics (2012)
  • Todd C. Headrick, Southern Illinois University Carbondale
  • Mohan D. Pant, University of Texas at Arlington
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.
Publication Date
Spring March 5, 2012
Citation Information
Todd C. Headrick and Mohan D. Pant. "On the Order Statistics of Standard Normal-Based Power Method Distributions" ISRN Applied Mathematics Vol. 2012 (2012)
Available at: http://works.bepress.com/mohan_pant/8/