Abstract
We perform a Bayesian analysis of the upper trunacated Zeghdoudi distribution based on type II censored data. Using various loss functions including the generalised quadratic, entropy and Linex functions, we obtain Bayes estimators and the corresponding posterior risks. As tractable analytical forms of these estimators is out of reach, we propose the use of simulations based on Markov chain Monte-carlo methods to study their performance. Given nitial values of model parameters, we also obtain maximum likelihood estimators. Using Pitmanw closeness criterion and integrated mean square error we compare their performance with those of the Bayesian estimators. Finally, we illustrate our approach through an example using a set of real data.
Highlights
Truncation is the process of excluding and omitting all the values that lay outside predetermined bounds in a statistical experiment
In the case of the generalized quadratic loss function, the Bayes estimators are given by the formulas: θGQ =
We note that the chosen value α = −2 provides the best posterior risks, which presents the best estimator for the generalised quadratic loss function case
Summary
Truncation is the process of excluding and omitting all the values that lay outside predetermined bounds in a statistical experiment. Aouf and Chadli (2017) considered the Bayesian inference under type II censored data of the generalized Lindley distribution. Boudjerda et al (2016) considered the Bayesian analysis under type II censored data of right truncated Weibull distribution. On Truncated Zeghdoudi Distribution: Posterior Analysis under Different Loss Functions for Type II Censored Data. It is widely used in modelling lifetime data including the series of papers by Zeghdoudi and Nedjar (2016a, 2016b, 2016c) where it is shown that it fits well a large class of real data sets. We propose a Bayesian analysis of the new upper truncated Zeghdoudi distribution.
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