Document Type : Research Manuscript
Authors
Department of Statistics, Payame Noor University (PNU), Tehran, Iran
Abstract
The Weighted Marshall-Olkin Bivariate Exponential (WMOBE) distribution was first proposed by
Jamalizadeh and Kundu (2013), who examined its different characteristics and properties. Bayesian
estimation of the model parameters is carried out using both the squared error loss (SEL) function,
which is symmetric, and the linear-exponential (LINEX) loss function, which is asymmetric. These
estimators are derived under both informative and non-informative gamma priors. Given the complexity
of the four-parameters model, explicit analytical solutions for the Bayesian estimators are not attainable,
making it necessary to employ the Gibbs sampling procedure. Markov Chain Monte Carlo (MCMC)
methods are widely utilized to compute and implement these estimates. Furthermore, the convergence
behavior of the Markov chain toward a stationary distribution is carefully analyzed. Credible intervals,
particularly the highest posterior density (HPD) intervals for the unknown parameters, are also
constructed. To assess and compare the effectiveness of these estimation approaches, Monte Carlo simulations are performed. Finally, the methodology is applied to a real-world dataset for illustrative purposes.
Keywords
- Bayesian estimation
- Markov Chain Monte Carlo
- Gibss sampling
- Weighted Marshall-Olkin Bivariate Exponential distribution
Main Subjects
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