Statistical Inference on the Power-Linear Hazard Rate Distribution Using Record Values: Estimation and Prediction

This article is devoted to the estimation and prediction problems on the power-linear hazard rate model using record values. The maximum likelihood technique and the Bayesian technique under the squared error, linear-exponential, and entropy loss functions are used for the point estimation of the parameters of this model. Also, the asymptotic confidence interval, two confidence intervals based on bootstrapping, as well as the highest posterior density confidence region are constructed for the interval estimation of the parameters. The problem of predicting future record values using the observed record data from the power-linear hazard rate distribution is investigated using both the maximum likelihood and Bayesian techniques. A real data set is analyzed in order to explain the estimation and prediction methods. Finally, a Monte Carlo simulation study is implemented to explore and compare the performance of the various discussed procedures. Based on our simulation results, it was observed that the performances of the Bayesian estimators and predictors under an informative prior and their corresponding confidence regions are more suitable in comparison with the other methods for most of the cases.