Mellin-Transform-Based New Results of the Joint Statistics of Partial Products of Ordered Random Variables

Abstract
Order statistics find applications in various areas including communications and signal processing. In this paper, we introduce new results of the joint statistics of partial products of ordered random variables (RVs) based on a Mellin-transform-based unified analytical framework. With the proposed approach, we can systematically derive the joint statistics of any partial products of ordered statistics, in terms of the Mellin transform and the probability density function (PDF). Our Mellin-transform-based approach can apply when all the K-ordered RVs are involved even for more complicated cases, when only the Ks (Ks <; K) best RVs are also considered. In addition, the closed-form expressions for the exponential RV special case are presented. As an application example, these results can apply to the performance analysis of various wireless communication systems over fading channels.

Citation
Nam, S. S., Ko, Y.-C., & Alouini, M.-S. (2017). Mellin-transform-based new results of the joint statistics of partial products of ordered random variables. 2017 IEEE International Symposium on Information Theory (ISIT). doi:10.1109/isit.2017.8006954

Conference/Event Name
2017 IEEE International Symposium on Information Theory (ISIT)

DOI
10.1109/ISIT.2017.8006954

Additional Links
https://ieeexplore.ieee.org/document/8006954

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