Statistical Inference of Two-Parameter Pareto Distribution under Double Type-I Hybrid Censoring Scheme

Based on a new lifetime testing scheme proposed in this paper, that is, double type-I hybrid censoring scheme, the maximum likelihood estimates of the parameters are obtained for two-parameter Pareto distribution. Also, the asymptotic confidence interval of \theta is obtained from Fisher information. When \alpha is known, the Bayesian and E-Bayesian estimates of \theta, as well as the Bayesian estimates of reliability function under different loss functions are obtained using the Gamma prior distribution. When both \alpha and \theta are unknown, the joint noninformation prior distribution is taken, and the Bayesian estimates of \alpha and \theta are calculated under the squared error loss function. Using Monte Carlo method to simulate the double type-I hybrid censored samples, the estimates of the unknown parameters and reliability function are obtained, with the increase of the sample size, the relative errors and the lengths of the confidence interval decrease gradually. Finally, a numerical example is analyzed.