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Posterior Properties of the Nakagami-m Distribution Using Noninformative Priors and Applications in Reliability

The Nakagami-m distribution plays an important role in problems related to communication engineering. This distribution can also be used for modeling reliability data as its hazard rate (mean residual life) function presents increasing (decreasing) or bathtub (unimodal) shapes. In this study, a Bayesian inference considering objective priors for the Nakagami-m distribution parameters is presented. We propose a theorem with sufficient and necessary conditions so that a general class of posteriors are proper. The impropriety of these posteriors can be observed by the behavior of the objective priors. This theorem is applied to different objective priors such as Jeffreys’ rule, Jeffreys prior, maximal data information prior, and reference priors. Simulation studies were conducted to investigate the performance of the Bayes estimators. Finally, our methodology is illustrated using two real lifetime datasets showing that the Nakagami-m distribution can be used to describe lifetime data.