Efficient estimation in the Pareto distribution with the presence of outliers

The maximum likelihood (ML) and uniformly minimum variance unbiased estimators (UMVUE) of the probability density function (pdf), cumulative distribution function (cdf) and rrth moment are derived for the Pareto distribution in the presence of outliers. It has been shown that MLE of pdf and cdf are better than their UMVUEs. At the end, these methods are illustrated with the help of real data from an insurance company.