A Statistical Study on the Parameters of the Skew Normal Distribution Depending on the Use of the Genetic Algorithm Using the Simulation Method

Abstract

Recent statistical research has witnessed activity on the study of skew normal distribution (SND) due to the fact that the data set does not fit well with the normal distribution due to Skewnessand excessive Kurtosis. For the purpose of estimating the parameters of the model (SND), the maximum likelihood method (ML) was used, but the probability equations of this method do not have clear solutions in the distribution (SND), and the problem was solved using the genetic algorithm (GA) and Other repetitive techniques are Newton Raphson, Nelder Mead and Iteratively Reweighting Algorithm, using the simulation method with different sample sizes and comparing the preference of results methods used based on criteria (Mean, Mse and Def). It has been concluded that (ML) capabilities using the (GA) of parameters (SND) are best in the case of a small or medium sample size and the best (IR) algorithm at a large sample size.