Classical estimation of hazard rate and mean residual life functions of Pareto distribution

Abstract

In this paper we find the maximum likelihood estimates (MLEs) of hazard rate and mean residual life functions (MRLF) of Pareto distribution, their asymptotic non degenerate distribution, exact distribution and moments. We also discuss the uniformly minimum variance unbiased estimate (UMVUE) of hazard rate function and MRLF. Finally, two numerical examples with simulated data and real data set, are presented to illustrate the proposed estimates.     

The Beta-Dagum Distribution: Definition and Properties

This article introduces a five-parameter Beta-Dagum distribution from which moments, hazard and entropy, and reliability measures are then derived. These properties show the high flexibility of the said distribution. The maximum likelihood estimators of the Beta-Dagum parameters are examined and the expected Fisher information matrix provided. Next, a simulation study is carried out which shows the good performance of maximum likelihood estimators for finite samples. Finally, the usefulness of the new distribution is illustrated through real data sets.