Mellin-transform-based new results of the joint statistics of partial products of ordered random variables

Sung Sik Nam; Young Chai Ko; Mohamed Slim Alouini

doi:10.1109/ISIT.2017.8006954

Mellin-transform-based new results of the joint statistics of partial products of ordered random variables

Sung Sik Nam, Young Chai Ko, Mohamed Slim Alouini

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

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.

Original language	English (US)
Title of host publication	2017 IEEE International Symposium on Information Theory, ISIT 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2373-2377
Number of pages	5
ISBN (Electronic)	9781509040964
DOIs	https://doi.org/10.1109/ISIT.2017.8006954
State	Published - Aug 9 2017
Event	2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: Jun 25 2017 → Jun 30 2017

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Conference

Conference	2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/Territory	Germany
City	Aachen
Period	06/25/17 → 06/30/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Applied Mathematics
Modeling and Simulation

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10.1109/ISIT.2017.8006954

Cite this

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. In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 2373-2377). Article 8006954 (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006954

Nam, Sung Sik ; Ko, Young Chai ; Alouini, Mohamed Slim. / Mellin-transform-based new results of the joint statistics of partial products of ordered random variables. 2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 2373-2377 (IEEE International Symposium on Information Theory - Proceedings).

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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.",

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Nam, SS, Ko, YC & Alouini, MS 2017, Mellin-transform-based new results of the joint statistics of partial products of ordered random variables. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006954, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 2373-2377, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 06/25/17. https://doi.org/10.1109/ISIT.2017.8006954

Mellin-transform-based new results of the joint statistics of partial products of ordered random variables. / Nam, Sung Sik; Ko, Young Chai; Alouini, Mohamed Slim.
2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 2373-2377 8006954 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

AB - 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.

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Nam SS, Ko YC, Alouini MS. Mellin-transform-based new results of the joint statistics of partial products of ordered random variables. In 2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 2373-2377. 8006954. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2017.8006954

Mellin-transform-based new results of the joint statistics of partial products of ordered random variables

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