On Stereographic Semi-circular Three Parameter Lindley Distribution With practical application

Abstract

In this paper, we found the semi-circular modified spherical inverse distribution (for a three-parameter Lindley distribution), which is concerned with converting ordinary (Cartesian) data into polar data (measured by angles) and then finding the characteristics of the semi-circular modified spherical inverse distribution (for a three-parameter Lindley distribution). The parameters of the new distribution are then estimated based on the Maximum Likelihood method and the fractional interval method. For the purpose of comparing the methods of estimating the parameters of the proposed distribution, the Monte Carlo simulation method was employed using a program in the MATLAB language to conduct several experiments with sample sizes. Different sizes (small (30), medium (50) and large (150,100)) based on the statistical standard Mean Squared Error (MSE). The results showed the superiority of the maximum likelihood method in calculating the estimates of the parameters of the proposed distribution under medium and large sample sizes and the superiority of the small method. And medium.