Bayesian Analysis of Unit Log-Logistic Distribution Using Non-Informative Priors

Mohammed K. Shakhatreh () and Mohammad A. Aljarrah
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Mohammed K. Shakhatreh: Department of Mathematics and Statistics, Faculty of Science, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan
Mohammad A. Aljarrah: Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan

Mathematics, 2023, vol. 11, issue 24, 1-18

Abstract: The unit log-logistic distribution is a suitable choice for modeling data enclosed within the unit interval. In this paper, estimating the parameters of the unit-log-logistic distribution is performed through a Bayesian approach with non-informative priors. Specifically, we use Jeffreys, reference, and matching priors, with the latter depending on the interest parameter. We derive the corresponding posterior distributions and validate their propriety. The Bayes estimators are then computed using Markov Chain Monte Carlo techniques. To assess the finite sample performance of these Bayes estimators, we conduct Monte Carlo simulations, evaluating their mean squared errors and their coverage probabilities of the highest posterior density credible intervals. Finally, we use these priors to obtain estimations and credible sets for the parameters in an example of a real data set for illustrative purposes.

Keywords: unit log-logistic distribution; Jeffreys prior; reference priors; probability matching priors; predictive p -value (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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