BAYESIAN AND NON-BAYESIAN ANALYSIS FOR THE BURR TYPE XII DISTRIBUTION BASED ON RECORD VALUES AND INTER-RECORD TIMES

Abstract

In many real life experiments, the only available data is a successive minimum (maximum) that is record-breaking data. In this paper, we obtain the maximum likelihood and Bayesian estimator of the shape parameter for Burr Type XII distribution based on lower record values and inter-record times (the number of trials following the record values) when the other one is known. In the Bayesian case, the estimates are derived under the squared error and the linear-exponential loss functions by using the informative and non informative priors. To be able to generate such a record-breaking data an inverse sampling or random sampling schemes can be used. In this paper, we assume that the record-breaking data are being generated by inverse sampling scheme. By using a Monte Carlo simulation methods: (i) the maximum likelihood and Bayes estimators are compared in terms of the estimated risk, (ii) the estimators are compared with and without the inter-record times are taken into consideration.