Estimation Methods for the Modified Generalized Linear Exponential Distribution and Its Applications in Engineering Data

Abstract

This paper investigates different methods for estimating the unknown parameters of the modified generalized linear exponential distribution (MGLED), a flexible lifetime model that can accommodate bathtub-shaped, increasing, and decreasing hazard rate functions. The MGLED is of practical importance in reliability and engineering applications because it includes several well-known lifetime distributions as special cases, such as the exponential, Rayleigh, Weibull, modified Weibull, and generalized linear exponential distributions. Five classical estimation methods are considered, namely maximum likelihood estimation, least squares estimation, weighted least squares estimation, Cramer von-Mises estimation, and Anderson-Darling estimation. The performance of these estimation methods is assessed through two real engineering data sets and an extensive simulation study. For the real data applications, the fitted models are compared using non-parametric goodness-of-fit measures, including the Kolmogorov-Smirnov statistic with its corresponding P-value, the Anderson-Darling statistic, and the Cramer von-Mises statistic. In addition, parametric model selection criteria, including the Akaike information criterion, the corrected Akaike information criterion, and the Hannan-Quinn information criterion, are used to evaluate the adequacy of the MGLED relative to several competing lifetime models. The simulation study compares the proposed estimation methods in terms of mean squared error and average absolute bias. The numerical results show that the MGLED provides a better fit than the competing models for the considered engineering data sets, while the simulation results indicate that the maximum likelihood estimation and Anderson-Darling estimation methods generally perform better than the other estimation methods as the sample size increases.