This paper deals with a new model called the power log-logistic modified Weibull distribution (PLLoGMWD) using the power transformation method, which can be regarded as an extension of the distribution introduced by Broderick O. Oluyede et al. Several significant statistical properties of the power log-logistic modified Weibull distribution are computed, including reliability, hazard rate functions, reverse hazard function, rth moment, characteristic function, Renyi entropy, conditional moments, and the reliability stress strength model. The distribution function, density function, hazard rate function and reliability of the new model have several interesting properties, which are illustrated in the graphs of each function. The estimation of model parameters is justified using the generalized method of moments, accompanied by a Monte Carlo simulation study to test the suitability of the proposed distribution. A comprehensive numerical simulation was conducted using nine different scenarios and two sample sizes, n = 100 and n = 500. It was observed that the performance of the estimators, especially for large samples, was less biased and more stable, ranging between –0.432 and 0.573. It also showed a significant decrease in mean square error values, ranging from 0.073 to 1.534, and mean absolute square error values, ranging from 0.298 to 1.654, offering the accuracy and robustness of the proposed model. Confidence intervals for the unknown parameters were calculated, ranging from 1.427 to 4.964. The results revealed in terms of bias, mean estimate, confidence intervals, mean absolute errors, and mean squared errors to demonstrate its future applicability in some real- life situations, especially, in the economic fields.
Jumana A. Altawil (Mon,) studied this question.