Parameter Estimation and Bayesian Prediction in the Log-logistic Distribution under Type-II Censored Data

Wassim Abou Ghaida^1, and Ayman Baklizi²

¹Foundation Program Unit, University of Doha for Science and Technology, Doha, Qatar

²Department of Statistics, Yarmouk University, Irbid, Jordan

Cite this paper:
Wassim Abou Ghaida and Ayman Baklizi. Parameter Estimation and Bayesian Prediction in the Log-logistic Distribution under Type-II Censored Data. International Journal of Business and Risk Management. 2025; 6(1):11-18. doi: 10.12691/ijbrm-6-1-1

Abstract

We consider Bayesian inference and point prediction in log-logistic distribution based on type-II censored data. We assume that the scale and shape parameters have independent gamma priors. The Bayes estimators cannot be obtained in closed form; therefore, we use Metropolis Hasting algorithm to approximate the Bayes estimates of the unknown scale and shape parameters. We compare the performance of the Bayes estimator with the Maximum Likelihood estimators. In addition, we obtained the Bayesian credibility intervals and compared them with the Wald intervals. Moreover, we derived Bayesian point and interval predictors for future observation and investigated their performance using simulation techniques. And finally, we analysed real data set for illustration purposes.

Keywords:
Bayes estimates Maximum Likelihood estimators Metropolis Hasting algorithm Predictive density Bayesian prediction Prediction interval

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