Bayesian Prediction of Future Order Statistics and k-Record Values based on Progressive Type-II Censored Sample for Generalized Exponential distribution

Bayesian Prediction of Future Order Statistics and k-Record Values

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

In this paper, we consider the problem of two-sample Bayesian prediction of order statistics and lower k-record values from a future sample arising from a generalized exponential distribution based on progressively type-II censored sample. We obtain the Bayesian point predictors based on squared error and linex loss functions. It is observed that the predictors cannot be obtained in closed forms. So we propose importance sampling method to obtain the estimators for both point and interval predictors.