<p>Estimating the parameters of the generalized logistic distribution has posed a challenge for many inference approaches, particularly in the frequentist approach. Surprisingly, there have been very few attempts to study the objective Bayesian analysis approach for this problem. In our study, we investigate objective Bayesian analysis using Jeffreys prior, reference priors, matching priors, and the maximal data information prior. We demonstrate that using these non-informative priors does not result in proper posterior distributions. Additionally, we develop a Bayesian analysis based on reference priors with partial information, which yields proper posterior distributions. To evaluate the performance of these priors, we conduct a small Markov Chain Monte Carlo (MCMC) study examining three of these prior distributions. The results demonstrate strong performance in terms of mean squared error and coverage probability. Finally, we utilize these priors to obtain estimations and credible sets for the distribution parameters in a specific example.</p>

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Objective Bayesian Analysis for the Generalized Logistic Distribution

  • Mohammed K. Shakhatreh,
  • Daojiang He

摘要

Estimating the parameters of the generalized logistic distribution has posed a challenge for many inference approaches, particularly in the frequentist approach. Surprisingly, there have been very few attempts to study the objective Bayesian analysis approach for this problem. In our study, we investigate objective Bayesian analysis using Jeffreys prior, reference priors, matching priors, and the maximal data information prior. We demonstrate that using these non-informative priors does not result in proper posterior distributions. Additionally, we develop a Bayesian analysis based on reference priors with partial information, which yields proper posterior distributions. To evaluate the performance of these priors, we conduct a small Markov Chain Monte Carlo (MCMC) study examining three of these prior distributions. The results demonstrate strong performance in terms of mean squared error and coverage probability. Finally, we utilize these priors to obtain estimations and credible sets for the distribution parameters in a specific example.