Inference and Simulation Study for the Exponentiated Novel α-Power Gumbel Model

Abstract

This study introduces and investigates a new flexible lifetime model, termed the Exponentiated Novel α-Power Gumbel (ENAPG) distribution, by applying the exponentiation technique to the recently proposed novel α-power Gumbel model. The proposed distribution extends the classical Gumbel family through the inclusion of an additional shape parameter, thereby enhancing its flexibility for modeling right-skewed and heavy-tailed data. To establish its theoretical usefulness, the study derives key statistical properties of the ENAPG distribution, including the survival and hazard rate functions, quantile function, moments, moment-generating function, Rényi and Tsallis entropies, and order statistics. Parameter estimation is carried out using the maximum likelihood estimation approach, with the resulting nonlinear likelihood equations solved numerically through iterative optimization routines. A comprehensive Monte Carlo simulation is further conducted to assess the finite-sample performance of the estimators across different sample sizes using bias, mean square error, root mean square error, and mean relative error criteria. The results indicate that the maximum likelihood estimators exhibit consistency and improved efficiency as sample size increases. Overall, the ENAPG distribution provides a robust and flexible alternative to existing Gumbel-type models and offers potential applications in reliability analysis, survival studies, and extreme-value modeling.