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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.

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