Bayesian and classical inference in Maxwell distribution under adaptive progressively Type-II censored data

In the reliability theory and life testing experiments, the Maxwell distribution has established a useful lifetime model due to its increasing failure rate property. To save time and money various types of censoring plans are studied in the literature. One such censoring scheme is adaptive progressive Type-II censoring (APT2C). It has recently become popular in life-testing experiments. The APT2C is a generalization of the progressive censoring scheme and it is very useful in various practical situations when testing material has a long life and high cost. This article deals with the problem of Bayesian and non-Bayesian estimation procedures of the unknown parameter and reliability characteristics of Maxwell distribution under the APT2C scheme. The maximum product spacing and the maximum likelihood estimates of the unknown parameters are obtained in the classical approach. In the Bayesian approach, the Bayes estimates are obtained under squared error loss function and linear exponential loss function with two choices of prior densities, non-informative and informative priors, respectively. The Bayes estimates are calculated using Tierney-Kadanae’s approximation and the Metropolis-Hastings algorithm. The asymptotic confidence interval, bootstrap confidence interval, and highest posterior density (HPD) credible interval are constructed for the interval estimation in the case of classical and Bayesian estimation procedures, respectively. Various estimates obtained in the theory are compared with the help of a Monte Carlo simulation study. Finally, a real data set is studied to show the applicability of the considered model.