Abstract
The need of new life time distributions that can be used to fit real data sets is crucial in lifetime data analysis. This article uses the two parameter bathtub (TPBT) and the gen-eralized exponential (GE) distributions to propose a new family of lifetime distributions, named the odd generalized exponential two-parameter bathtub shaped distribution (OGE-TPBT). Statistical properties of the proposed distribution are discussed. The maximum like-lihood and Bayesian procedures are used to estimate the model's parameters and some of its reliability measures. For Bayes method, we use three approaches of the approximate Bayesian computation (ABC) method. Simulation study is provided to investigate the prop-erties of the methods applied. Based on some well know diagnostic tests, we find out that the simulation data provided in this paper is appropriate. To discuss the possible improve-ments of the new distribution compared to the original two distributions (GE and TPBT) and its applicability, a real-life data set is analyzed. Based on the comparison results, we found out that the OGE-TPBT fits the data better than both the GE and TPBT distributions. Also, we used the same real data set to compare the three approaches of the ABC. Based on the comparisons results of these three approaches, we recommend the naive ABC to approximate Bayes estimations in the situation for which there is no analytic solution.(c) 2022 The Author(s). Published by Elsevier B.V. on behalf of African Institute of Mathematical Sciences / Next Einstein Initiative. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )