Order Statistics and ML Estimators of a 3-Component Mixture of Power Distribution: A Simulation Study

Abstract

The probability density functions of , and order statistics are explored in this study. Also, the moments, their mean and variance of , and order statistics are derived. The Maximum Likelihood (ML) method is employed to estimate the parameters, and a system of non-linear equations is solved to derive the limiting expressions of the ML estimators and their variances, utilizing Fisher’s information matrix. A detailed numerical analysis of the ML estimators’ performance is carried out through a Monte Carlo simulation for various sample sizes, test termination times, and parameter values. Additionally, the practical applicability of the 3-component mixture of Power distributions is demonstrated by estimating the ML parameters using real-world data. The study's results indicated that maximum likelihood estimators based on complete (uncensored) data perform significantly better than those based on censored data. Additionally, the estimators derived from uncensored data are more dependable and precise.