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

Author

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  • Yousuf Abo Rahama

    (American University of Sharjah)

  • Mahmoud H. Ismail

    (American University of Sharjah
    Cairo University)

  • Mohamed S. Hassan

    (American University of Sharjah)

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.

Suggested Citation

  • Yousuf Abo Rahama & Mahmoud H. Ismail & Mohamed S. Hassan, 2018. "On the distribution of the product and ratio of products of EGK variates with applications," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 68(2), pages 231-238, June.
    • Handle: RePEc:spr:telsys:v:68:y:2018:i:2:d:10.1007_s11235-017-0389-x
    DOI: 10.1007/s11235-017-0389-x
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    References listed on IDEAS

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    1. Mridula Garg & Ajay Sharma & Pratibha Manohar, 2016. "The distribution of the product of two independent generalized trapezoidal random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(21), pages 6369-6384, November.
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