Bayesian Estimation and Prediction for Discrete Alpha Power Inverted Kumaraswamy Distribution

نوع المستند : المقالة الأصلية

المؤلفون

1 1Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt

2 Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt

3 2Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt

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Abstract
      This paper discusses the Bayesian estimation for the parameters, survival, hazard rate and alternative hazard rate functions of the three unknown parameter of the discrete alpha power inverted Kumaraswamy distribution when the lifetimes are Type-II censored. The independent exponential prior for the alpha power parameter and the joint bivariate prior for the shape parameters of the inverted Kumaraswamy distribution is used to obtain the posterior distributions. The estimators are derived under squared error and linear-exponential loss functions. Credible intervals for the parameters, survival, hazard rate and alternative hazard rate functions are obtained. Bayesian prediction (point and interval) for the future observation is investigated under the two-sample prediction Scheme. The efficiency of the Bayes estimates is investigated, through some measurements of accuracy for different sample sizes. Regarding the results of the simulation study, it seems to perform better when the sample size increases and the level of censoring decreases. Also, in most cases the results under the linear-exponential loss function is better than the corresponding results under squared error loss function. Two real data sets are applied to ensure the theoretical results and confirm its applicability to real life applications.  to compare the efficiency of these estimators under different loss functions.
 

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