Statistical inference of exponentiated Pareto distribution under adaptive type-II progressive censored schemes

Abstract

In order to guarantee the efficiency of life and reliability test in the case of censored data, and to control the total test time, an adaptive type-II progressive censored scheme is discussed. In this article, the classical estimation methods and Bayesian estimation methods are used to estimate the two unknown parameters, reliability function and hazard function of the Exponentiated Pareto distribution. In addition to the maximum likelihood estimation, the stochastic expectation-maximization (SEM) algorithm is also applied. Under two different loss functions, Lindley’s approximation and importance sampling method are used to obtain Bayesian estimates. The Bayesian credible interval is constructed while the Bayesian estimate is evaluated by the Metropolis-Hastings method. The Monte Carlo method is applied to compare the performance of the estimation methods. Then a real life data set is analyzed. Finally, the selection criteria of various estimation methods are proposed.

Keywords:

• Adaptive type-II progressive censored schemes
• Exponentiated Pareto distribution
• Importance sampling method
• Lindley’s approximation
• Maximum likelihood estimation
• Metropolis-Hastings method
• SEM algorithm

Acknowledgements

The authors would like to thank the editor and anonymous referees for their constructive comments and suggestions that have substantially improved the original manuscript.

Additional information

Funding

The authors' work was partially supported by the Fundamental Research Funds for the Central Universities (2021YJS163) and the National Statistical Science Research Project of China (No. 2019LZ32).