On The Distribution of The Ratio of Two Hyper-Erlang Random Variables

Authors

Therrar Kadri, Department of Mathematics, Lebanese International University, LebanonFollow
Khaled Smaili, Department of Mathematics, Lebanese International University, LebanonFollow
Seifedine Kadry, Department of Mathematics, Lebanese University, LebanonFollow

Author Country (or Countries)

Lebanon

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. Moreover, the particular case, the ratio of two independent Hyper-Exponential distribution is examined.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110121

Recommended Citation

Kadri, Therrar; Smaili, Khaled; and Kadry, Seifedine (2017) "On The Distribution of The Ratio of Two Hyper-Erlang Random Variables," Applied Mathematics & Information Sciences: Vol. 11: Iss. 1, Article 21.
DOI: http://dx.doi.org/10.18576/amis/110121
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss1/21