Some Computational Aspects to Find Accurate Estimates for the Parameters of the Generalized Gamma distribution

TL;DR

This paper explores computational methods to improve parameter estimation for the generalized gamma distribution, addressing issues with maximum likelihood and Bayesian approaches, especially in censored data scenarios.

Contribution

It introduces techniques for selecting initial values and priors to enhance the stability and accuracy of parameter inference for the generalized gamma distribution.

Findings

Proposed methods improve estimation stability.

Techniques are effective with censored data.

Enhanced Bayesian prior elicitation methods.

Abstract

In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no stable behavior depending on large sample sizes and good initial values to be used in the iterative numerical algorithms. From a Bayesian approach, this problem remains, but now related to the choice of prior distributions for the parameters of this model. We presented some exploratory techniques to obtain good initial values to be used in the iterative procedures and also to elicited appropriate informative priors. Finally, our proposed methodology is also considered for data sets in the presence of censorship.