On estimation for the Pareto distribution

In this work, we obtain the rr-th raw moments of the probability density function (PDF) and reliability function (RF) for the Pareto distribution under the maximum likelihood estimation (MLE) and uniform minimum variance unbiased estimation (UMVUE). We derive some large sample properties of the estimators, the MLE and UMVUE of the PDF as well as RF. Two examples are provided to compute the efficient estimations of PDF and RF numerically. Our results indicate that there are no absolute superiorities of MLEs over the UMVUEs of PDF and RF and vice versa.