The uniform minimum variance unbiased (UMVU), maximum likelihood (ML), Moment (MM), quantile (MQ) and least squares (LS) estimations of the probability density function (pdf), cumulative distribution function (CDF) and rth moment are derived for the exponentiated Pareto distribution in the presence of outliers. It has been shown that MLE is better than UMVUE and UMVUE is better than the others. Also, UMVU and ML estimators of rth moment are more efficient than its MQ and LS estimators. Further, it is shown that for high value of sample size, UMVUE of rth moment is better than MLE. In the last, we have given an example with actual data from an insurance company.

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