Evaluation and Comparison of Metaheuristic Methods to Estimate the Parameters of Gamma Distribution

Abstract

Parameter estimation of three parameter (3-p) Gamma distribution is very important as it is one of the most popular distributions used to model skewed data. Maximum Likelihood (ML) method based on finding estimators that maximize the likelihood function, is a well-known parameter estimation method. It is rather difficult to maximize the likelihood function formed for the parameter estimation of the 3-p Gamma distribution. In this study, five well known metaheuristic methods, Simulated Annealing (SA), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and Artificial Bee Colony (ABC), are suggested to obtain ML estimates of the parameters for the 3-p Gamma distribution. Monte-Carlo simulations are performed to examine efficiencies of the metaheuristic methods for the parameter estimation problem of the 3-p Gamma distribution. Also, differences between solution qualities and computation time of the algorithms are investigated by statistical tests. Moreover, one of the multi-criteria decision-making methods, Technique for Order Performance by Similarity to Ideal Solution (TOPSIS), is preferred for ranking the metaheuristic algorithms according to their performance in parameter estimation. Results show that Differential Evolution is superior to the others for this problem in consideration of all the criteria of solution quality, computation time, simplicity, and robustness of the metaheuristic algorithms. In addition, an analysis of real-life data is presented to demonstrate the implementation of the suggested metaheuristic methods.