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

Yousuf Abo Rahama, Mahmoud H. Ismail () and Mohamed S. Hassan
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Yousuf Abo Rahama: American University of Sharjah
Mahmoud H. Ismail: American University of Sharjah
Mohamed S. Hassan: American University of Sharjah

Telecommunication Systems: Modelling, Analysis, Design and Management, 2018, vol. 68, issue 2, No 8, 238 pages

Abstract: 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- $$\mathcal {K}$$ 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 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11235-017-0389-x

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