Three-parameter (3-p) Gamma distribution is one of the most commonly used distribution to model for life spans, reaction times, and other types of skewed data. Therefore, parameter estimation of this distribution is very important, especially in the application literature. Maximum Likelihood (ML) is the most popular method used to obtain estimators of unknown parameters, but it is rather difficult to obtain ML estimators for 3-p Gamma distribution since likelihood equations of this distribution do not have explicit solutions. Traditional iterative methods such as Newton Raphson and Nelder Mead could be used in this case. However, these methods have an initial value problem. To overcome this problem, ML estimation of the parameters of 3-p Gamma distribution has been conducted using Differential Evolution (DE) and Genetic Algorithms (GA), which are the two most popular evolutionary algorithms, in this study. Monte Carlo simulations have been performed to examine the efficiencies of these methods for the parameter estimation of the 3-p Gamma distribution. A comparison of these methods has been made by using statistical analysis with regards to solution quality and solution time. The results show that DE algorithm is better than the GA in terms of solution quality and there is no statistically significant difference between these two methods in terms of solution time.
Anahtar Kelimeler: Differential Evolution Algorithm, Three Parameter Gamma Distribution, Genetic Algorithm, Maximum Likelihood Estimation, Monte Carlo Simulation.