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A Bayesian Analysis for the Parameters of the Exponential-Logarithmic Distribution

Summary: The exponential-logarithmic is a new lifetime distribution with decreasing failure rate and interesting applications in the biological and engineering sciences. Thus, a Bayesian analysis of the parameters would be desirable. Bayesian estimation requires the selection of prior distributions for all parameters of the model. In this case, researchers usually seek to choose a prior that has little information on the parameters, allowing the data to be very informative relative to the prior information. Assuming some noninformative prior distributions, this article presents a Bayesian analysis using Markov chain Monte Carlo (MCMC) methods. The Jeffreys prior is derived for the parameters of exponential-logarithmic distribution and compared with other common priors such as beta, gamma, and uniform distributions. The article shows through a simulation study that the maximum likelihood estimate may not exist except under restrictive conditions. In addition, the posterior density is sometimes bimodal when an improper prior density is used.

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  • Topics: Engineering, Statistics, Quality Tools
  • Keywords: Bayesian methods, Exponential distribution, Markov chains, Monte Carlo methods, Posterior, Failure rate, Lifetime data, Parametric models
  • Author: Moala, Fernando A.; Garcia, Lívia M.;
  • Journal: Quality Engineering