Asian Journal of Pure and Applied Mathematics

Flexible lifetime distributions are crucial for modeling skewed and heavy-tailed data commonly encountered in reliability, environmental studies, and risk modeling. The practical utility of these models depends on efficient parameter estimation methods that provide accurate and stable estimates, particularly for distributions with complex likelihoods. This study presents a comparative analysis of three parameter estimation methods—Method of Moments (MM), Maximum Likelihood Estimation (MLE) method, and the Expectation-Maximization (EM) algorithm for the Transmuted Exponential-New Weibull Pareto (TE-NWP) distribution. The TE-NWP extends the New Weibull Pareto distribution by introducing a transmutation parameter, enhancing flexibility in modeling skewed and heavy-tailed lifetime data. Due to its five parameters, the TE-NWP likelihood function is highly nonlinear, making analytical solutions challenging. To assess estimator performance, a Monte Carlo simulation was conducted with sample sizes of n = 20, 100, and 500, using 1,000 replications per scenario to evaluate bias and mean squared error (MSE). The results indicate that the EM algorithm consistently yields smaller bias and lower MSE than the MM and MLE methods, particularly as the sample size increases. The estimation methods were further applied to Kevlar 373/epoxy fatigue fracture data. Based on the log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), the EM-based estimates provided the best fit to the data. These findings suggest that the EM algorithm is the most efficient approach for estimating TE–NWP parameters, and thus serves as a valuable tool for analyzing complex lifetime data in reliability and risk studies.