The Exact Distribution of The Ratio of Two Independent Hypoexponential Random Variables

The distribution of ratio of two random variables are of interest in many areas of the sciences. The study of the ratio of same family and finding their exact density expression was examined by many authors for decades. Some are solved and others gave approximations, but many still unsolved. In this paper, we consider the ratio of two independent Hypoexponential distributions. We find the exact expressions for the probability density function, the cumulative distribution function, moment generating function, the reliability function and hazard function, which was proved to be a linear combination of the Generalized-F distribution.