A novel approach in Multi-hop networks technology with the ratio distribution of two Hyper-Erlang random variables

  • Therrar Kadri Department of Mathematics, Faculty of Sciences, Lebanese International University, Al-Khyara, Lebanon.
  • Khaled Smaili Department of Applied Mathematics, Faculty of Sciences, Lebanese University, Zahle, Lebanon.
  • Seifedine Kadry American University of the middle east, Kuwait
DOI: https://doi.org/10.19139/soic.v3i4.143
Keywords: Ratio Distribution, Hyper-Erlang Distribution, Erlang Distrib- ution, Generalized-F Distribution, Log-logistic Distribution, Probability Den- sity Function, Survivor function, Moment Generating Function.

Abstract

The distribution of ratio of two random variables has been studied by several authors especially when the two random variables are independent and come from the same family. In this paper, the exact distribution of the ratio of two independent Hyper-Erlang distribution is derived. However, closed expressions of the probability density, cumulative distribution function, reliability function, hazard function, moment generating function and the rth moment are found for this ratio distribution and proved to be a linear combination of the Generalized-F distribution. Finally, we will apply our results to real life application in analyzing the performance of wireless communication systems.

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Published
2015-11-28
How to Cite
Kadri, T., Smaili, K., & Kadry, S. (2015). A novel approach in Multi-hop networks technology with the ratio distribution of two Hyper-Erlang random variables. Statistics, Optimization & Information Computing, 3(4), 312-321. https://doi.org/10.19139/soic.v3i4.143
Issue
Vol 3 No 4 (2015)
Section
Research Articles
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