Estimation and Prediction for the Power-Exponential Hazard Rate Distribution Based on Record Data

Synoptic Abstract The problems of classical and Bayesian estimation of the parameters of the power-exponential hazard rate distribution (P-EHRD) based on record values and the prediction of future record values are considered. The parameters of P-EHRD are estimated by the maximum likelihood and the least squares methods, and the Bayes estimates are obtained by the Metropolis-Hastings method under the squared error loss and LINEX loss functions. Also, an asymptotic confidence interval, two bootstrap confidence intervals and the highest posterior density (HPD) credible interval for the unknown parameters are constructed. The problem of predicting the future record values from the P-EHRD based on the past record values is considered using the maximum likelihood and Bayesian approaches. To investigate and compare the performance of the different proposed methods, a Monte Carlo simulation study is conducted. Finally, an example is presented to illustrate the estimation and prediction procedures.