Exact distribution of time between failures under gamma lifetime model

This paper is concerned with the distribution of the time between failures (TBF) under the gamma lifetime model. The exact distribution of TBF is computed in closed form. This allows interested researchers to compute the reliability of certain system models. To better visualize the distributions of TBF, its probability distribution function (pdf) is represented using matrices. Moreover, the moments of TBF is computed and given in closed form. Wolfram Mathematica cods are given in the appendix for fast and easy implementation. Finally, simulation studies for the TBF are performed together with relative tests results.