Abstract
In this article, we proposed a new four-parameter distribution called beta Erlang truncated exponential distribution (BETE). Some important mathematical and statistical properties of the proposed distribution are examined. The stochastic ordering result for the BETE was also discussed. Moreover, the rth moment, moment generating function, incomplete moments, mean deviations, Bonferroni and Lorenz curves, moments of residual life, Shannon and Renyi entropies, and Kullback-Leibler divergence measure are derived. The maximum-likelihood estimate for the unknown parameters of the BETE was established and assessed by the simulation studies. The maximum likelihood estimation of the stress-strength parameter is discussed and its asymptotic distribution is obtained. The effectiveness and usefulness of the BETE are demonstrated by the use of three real data set, in which the BETE provide a better fit than some other existing distributions and demonstrated its capability in the stress-strength reliability analysis.