A Modified Reference Prior for the Generalized Gamma Distribution

TL;DR

This paper introduces a modified reference prior for the generalized gamma distribution to ensure proper posterior distributions in Bayesian estimation, validated through simulations and real data analysis.

Contribution

It proposes a novel modification to the reference prior, enabling proper Bayesian inference for the generalized gamma distribution.

Findings

Modified prior yields proper posteriors

Simulation confirms efficiency of the method

Real data application demonstrates practical utility

Abstract

In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome this problem by proposing a modification in a reference priori distribution, allowing for a proper posterior distribution for the parameters of the generalized gamma distribution. We perform a simulation study in order to study the efficiency of the proposed methodology, which is also fully illustrated on a real data set.