Some Statistical Inference for Pareto Distribution Under Simple Random Sampling in the Presence of Outliers

Pareto is a continuous distribution which has several applications in real life fields including the extreme value events. Hence, in this paper, the maximum likelihood (ML) and method of moment (MOM) estimations are proposed to estimate the shape parameter estimates for Pareto Type I distribution. The BIAS, Mean Square Error (MSE), and the Standard Error (SE) of the shape parameter estimates for both the two methods were obtained based on different simulated sample sizes. The scale parameter of Pareto distribution is treated as a fixed value. In this paper, the data is contaminated with 5% and 10% of outliers to investigate the effect of the outliers on the parameter estimates. The results show that when the sample size was large, the parameter estimates were more reliable and accurate. However, in the presence of outliers, the method of moment is better than the maximum likelihood estimation evident by having the smallest standard errors.