Inference on Nadarajah–Haghighi distribution with constant stress partially accelerated life tests under progressive type-II censoring

Abstract

This paper presents methods of estimation of the parameters and acceleration factor for Nadarajah–Haghighi distribution based on constant-stress partially accelerated life tests. Based on progressive Type-II censoring, Maximum likelihood and Bayes estimates of the model parameters and acceleration factor are established, respectively. In addition, approximate confidence interval are constructed via asymptotic variance and covariance matrix, and Bayesian credible intervals are obtained based on importance sampling procedure. For comparison purpose, alternative bootstrap confidence intervals for unknown parameters and acceleration factor are also presented. Finally, extensive simulation studies are conducted for investigating the performance of the our results, and two data sets are analyzed to show the applicabilities of the proposed methods.

Keywords:

• Maximum likelihood estimator
• bootstrap confidence intervals
• credible intervals
• Bayes estimates

Classification AMS (2010):

• Primary 62F10
• 62F15
• Secondary 62N02

Acknowledgments

The authors would like to thank the editor, associated editor and the referees for their insightful comments that have led to a substantial improvement to an earlier version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work of Liang Wang was supported by National Natural Science Foundation of China [grant number 12061091 and China Postdoctoral Science Foundation [grant number 2019M650260].