Asymptotic Value of the Probability That the First Order Statistic Is from Null Hypothesis

Iickho Song, Seungwon Lee, So Ryoung Park, Seokho Yoon

College of Information and Communication Engineering, Sungkyunkwan University, Suwon, South Korea.
Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea.
School of Information, Communications, and Electronics Engineering, The Catholic University of Korea, Bucheon, South Korea.

DOI: 10.4236/am.2013.412231                

Abstract

When every element of a random vector X =(X₁,X₂,^...,X_n) assumes the cumulative distribution function F₀ and F₁ with probability p and 1 - p, respectively, we have shown that the probability S₀ that the first order statistic of X is originally under F₀ can be expressed as . We have also shown that , where  and   with  the support of F _i (x) . Applications and implications of the results are discussed in the performance of wideband spectrum sensing schemes.

Keywords

Energy; Order Statistic; Probability; Spectrum Sensing

Conflicts of Interest

The authors declare no conflicts of interest.

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