Bayesian estimation of discrete Burr distribution with two parameters

TL;DR

This paper develops a Bayesian approach to estimate parameters of the discrete Burr distribution with two parameters, using Metropolis-Hastings to handle the complex posterior distribution.

Contribution

It introduces a Bayesian estimation method for the two-parameter discrete Burr distribution, addressing the challenge of non-standard posterior distributions.

Findings

Successful implementation of Metropolis-Hastings algorithm for parameter estimation

Demonstrated the effectiveness of Bayesian estimates in this distribution

Provides a new approach for complex discrete distribution parameter estimation

Abstract

So far, various techniques have been implemented for generating discrete distributions based on continuous distributions. The characteristics and properties of this kind of probability distributions have been studied. Furthermore, the estimation of related parameters have been computed trough classical methods. However, a few studies addressed the parameter estimate issue of these distributions through Bayesian methods. This is essentially because of the complexity of the model whatever the number of parameter is and the fact that in general they contain a large number of parameters to be estimated. This paper deals with computing Bayes estimate of the parameters of discrete Burr distribution with two parameters. Since the resulting posterior distribution of the parameters is not standard, we apply Metropolis-Hastings algorithm to simulate from the posterior density.