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Bayesian Analysis of Power Function Distribution Using Different Loss Functions
Azam Zaka,Ahmad Saeed Akhter 보안공학연구지원센터 2014 International Journal of Hybrid Information Techno Vol.7 No.6
Power function distribution is a flexible lifetime distribution that may offer a good fit to some failure data sets. In this paper, we obtain Bayesian estimators of the shape parameter of Power function distribution. For the Posterior distribution of this parameter, we consider Exponential Prior, Pareto Prior, Chi-Square Prior, Quasi Prior and Extension of Jeffrey`s Prior. The three loss functions taken up are Squared Error Loss Function (SELF), Quadratic Loss Function (QLF) and Precautionary Loss Function (PLF). The performance of an estimator is assessed on the basis of its relative Posterior risk. Monte Carlo Simulations are used to compare the performance of the estimators. It is discovered that the PLF produces the least Posterior risk when Exponential and Pareto Priors are used. SELF is the best when Chi-Square, Quasi and Extension of Jeffrey`s Priors are used.