This study presents a new lifetime model known as the Transmuted Exponential-Weibull-Exponential (TE-W-E) distribution. The proposed model possesses a flexible structure that makes it well suited for analyzing positive data and accommodating a bathtub-shaped hazard rate function, which is common in survival analysis. Several fundamental mathematical properties of the new distribution are derived and presented in closed form. These include the ordinary moments, mean, variance, moment generating, quantile, survival, hazard, reversed hazard, odd, cumulative hazard functions, Rényi entropy, and order statistics. The parameter effects on descriptive statistics are examined and the findings show that they have effect on the distribution. The parameters of the proposed TE-W-E model are estimated using the maximum likelihood estimation method. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates in terms of bias, variance, and mean squared error across various sample sizes. The simulation results indicate that the maximum likelihood estimation method provides reliable estimates of the model parameters. To demonstrate the practical usefulness of the proposed distribution, it is fitted to two real lifetime datasets. The results show that the proposed TE-W-E model provides a superior goodness-of-fit compared to existing models, based on standard statistical evaluation criteria.

Keywords:Maximum likelihood, Transmuted Exponential-Weibull-Exponential, Weibull-Exponential, Weibull-Gamma, lifetime data