Many lifetime datasets encountered in reliability engineering, survival analysis, and other applied sciences exhibit complex characteristics such as skewness, heavy tails, elongation, and varying hazard rate structures, which render classical probability distributions inadequate for accurate modelling. To address this limitation, this study proposes a new flexible lifetime model, termed the Transmuted Exponential–New Weibull Pareto (TE–NWP) distribution, obtained by applying the Transmuted Exponential-G (TE–G) family to the New Weibull Pareto distribution. The proposed model possesses a flexible five-parameter structure suitable for analysing positive data and is capable of capturing skewed and heavy-tailed lifetime behaviours. In addition, the model exhibits a bathtub-shaped hazard rate function, providing greater flexibility in modelling datasets characterized by elongation and asymmetry compared to several existing distributions. Several important statistical properties of the distribution are derived, including the moments, moment generating function, quantile function, survival function, and hazard function. The model parameters are estimated using the maximum likelihood estimation (MLE) method. A Monte Carlo simulation study is conducted to evaluate the performance of the estimators in terms of bias, variance, and mean squared error under varying sample sizes. Finally, the applicability of the proposed distribution is demonstrated using two real-life datasets. The results indicate that the TE–NWP distribution provides a superior fit compared to several competing models based on information criteria and goodness-of-fit.

Keywords: Transmuted Exponential-G family, New Weibull Pareto distribution, Lifetime data, Maximum likelihood estimation, Heavy-tailed and skewed data