Maximum likelihood and maximum product of spacings estimations for the parameters of skew-normal distribution under doubly type II censoring using genetic algorithm

Abstract

In this study, we use the maximum likelihood (ML) and the maximum product of spacings (MPS) methodologies to estimate the location, scale and skewness parameters of the skew-normal distribution under doubly type II censoring. However, it is known that these estimators cannot be obtained analytically because of nonlinear functions in the estimating equations. Therefore, numerical methods such as Nelder–Mead (NM), Newton–Raphson (NR), iteratively re-weighting algorithm (IRA), etc., are used to overcome this problem. In this study, different than the earlier studies, we use the genetic algorithm (GA) which is a population-based heuristic method based on the random search to find the estimates of the unknown parameters. In constructing the search space for GA, we utilize the robust confidence intervals to have a high convergence rate in GA. Then, we compare the efficiencies of the ML estimators obtained by using NM, NR, IRA, and GA methods and the efficiencies of the MPS estimators obtained by using NM and GA methods via an extensive Monte-Carlo simulation study. At the end of the study, we analyze the deep-groove ball bearings data to show the implementation of the proposed methodology.