Highest posterior density estimation from multiply censored Pareto data

Abstract

In statistical practice, it is quite common that some data are unknown or disregarded for various reasons. In the present paper, on the basis of a multiply censored sample from a Pareto population, the problem of finding the highest posterior density (HPD) estimates of the inequality and precision parameters is discussed assuming a natural joint conjugate prior. HPD estimates are obtained in closed forms for complete or right censored data. In the general multiple censoring case, it is shown the existence and uniqueness of the estimates. Explicit lower and upper bounds are also provided. Due to the posterior unimodality, HPD credibility regions are simply connected sets. For illustration, two numerical examples are included.