Estimating the four parameters of the Burr III distribution using a hybrid method of variable neighborhood search and iterated local search algorithms

The Burr III distribution properly approximates many familiar distributions such as Normal, Lognormal, Gamma, Weibull, and Exponential distributions. It plays an important role in reliability engineering, statistical quality control, and risk analysis models. The Burr III distribution has four parameters known as location, scale, and two shape parameters. The estimation process of these parameters is controversial and puts a halt in front of statistical data analyzers. Although the maximum likelihood estimation (MLE) is understood as a straightforward method in parameters estimation, using MLE to estimate the Burr III parameters leads to maximize a complicated function with four unknown variables, where using a conventional optimization such as the gradient method is difficult. In this paper to circumvent the difficulty of maximizing the Burr III likelihood function, a meta-heuristics hybrid approach is proposed to estimate the unknown parameters. The hybrid approach composes of a variable neighborhood search (VNS) along with an iterated local search (ILS) algorithm to take part in the MLE method. In the proposed algorithm, different heuristic local search methods are investigated to promote the ILS algorithm performance. Furthermore, the Taguchi approach is employed to tune the parameters. The results of some numerical examples and simulation study indicate satisfactory performance of the proposed methodology.