Topp-Leone distribution with an application to binomial sampling

In this paper, we present the exact distribution of the sum of two independent Topp-Leone variables which becomes useful in calculating the exact reliability of a standby system with Topp-Leone distributed component units when the values of parameters are known. Applications in Bayesian analysis with binomial sampling are also considered, and the comparison of the performance of Beta and Topp-Leone priors is then made.