A Bayesian look at classical estimation: The shape of the pareto distribution and its functions.

The Pareto Distribution has been found to be useful in describing socio-economic, physical, and biological phenomena. This paper explores different methods of estimating the shape parameter of the Pareto distribution and two of its functions (reliability and hazard functions), assuming the scale parameter is known. In particular, this paper shows that the Bayesian approach, using both the quadratic and entropy loss functions, can provide a general method for estimating the shape parameter and these two functions. These Bayesian estimators generalize the maximum likelihood estimator (MLE) and the uniformly most powerful unbiased estimator (UMVUE). Simulation results show that the general Bayesian method can perform better than the MLE and UMVUE, especially when the sample size is small. [ABSTRACT FROM AUTHOR]