Comparison of Estimation Methods for the Inverted Exponentiated Pareto Distribution

Abstract

Inverted exponentiated exponential densities family is known for its flexibility and applicability in the reliability field. This study evaluates the performance of different estimation methods for the inverted exponentiated Pareto (IEP) distribution, which is a special case of this family of distributions. In this study, the parameter estimation of the IEP distribution is obtained using Maximum Likelihood (ML), Maximum Product of Spacings (MPS), Cramer von Mises (CvM), and Anderson Darling (AD) methods. A Monte Carlo simulation is conducted to compare the efficiency of these estimation methods, while real data applications from different fields are utilized to demonstrate practical performance. The fitting performance of the methods is assessed using metrics such as root mean squared error, coefficient of determination, Anderson Darling, and the Kolmogorov-Smirnov test. Simulation results indicate that the MPS method generally outperforms the ML and CvM methods, whereas real data applications reveal that the CvM method provides the best parameter estimates, followed by MPS.