Telecommunication Systems

, Volume 68, Issue 2, pp 231–238 | Cite as

On the distribution of the product and ratio of products of EGK variates with applications

  • Yousuf Abo Rahama
  • Mahmoud H. Ismail
  • Mohamed S. Hassan
Article
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Abstract

We derive novel exact closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the product and ratio of products of an arbitrary number of independent non-identically distributed (i.n.i.d) extended generalized-\(\mathcal {K}\) (EGK) variates. The expressions are given in terms of the Meijer’s G-function and can be computed easily using commonly available mathematical software tools. They also subsume those for arbitrary combinations of other well-known variates and can be directly utilized in performance evaluation of wireless communication systems under different scenarios. We present various analytical results that are verified via Monte-Carlo simulations for both the PDF and CDF as well as their application in multiple practical scenarios.

Keywords

EGK variates Fading channels Product of random variables Ratio of product of random variables 
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Notes

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Yousuf Abo Rahama
    • 1
  • Mahmoud H. Ismail
    • 1
    • 2
  • Mohamed S. Hassan
    • 1
  1. 1.Department of Electrical EngineeringAmerican University of SharjahSharjahUAE
  2. 2.Department of Electronics and Communications Engineering, Faculty of EngineeringCairo UniversityGizaEgypt

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