Systematic and Unified Stochastic Tool to Determine the Multidimensional Joint Statistics of Arbitrary Partial Products of Ordered Random Variables

Sung Sik Nam, Young Chai Ko, Duckdong Hwang, Mohamed Slim Alouini

Research output: Contribution to journalArticle


In this paper, we introduce a systematic and unified stochastic tool to determine the joint statistics of partial products of ordered random variables (RVs). With the proposed approach, we can systematically obtain the desired joint statistics of any partial products of ordered statistics in terms of the Mellin transform and the probability density function in a unified way. Our approach can be applied when all the K -ordered RVs are involved, even for more complicated cases, for example, when only the KsKs < K best RVs are also considered. As an example of their application, these results can be applied to the performance analysis of various wireless communication systems including wireless optical communication systems. For an applied example, we present the closed-form expressions for the exponential RV special case. We would like to emphasize that with the derived results based on our proposed stochastic tool, computational complexity and execution time can be reduced compared to the computational complexity and execution time based on an original multiple-fold integral expression of the conventional Mellin transform based approach which has been applied in cases of the product of RVs.

Original languageEnglish
Article number8844664
Pages (from-to)139773-139786
Number of pages14
JournalIEEE Access
Publication statusPublished - 2019 Jan 1



  • exponential random variables
  • information combining
  • Joint PDF
  • Mellin transform (MT)
  • order statistics
  • partial products
  • probability density function (PDF)

ASJC Scopus subject areas

  • Computer Science(all)
  • Materials Science(all)
  • Engineering(all)

Cite this