Estimation for an inverted exponentiated Rayleigh distribution under type II progressive censoring

Abstract

In this paper, we consider estimation of unknown parameters of an inverted exponentiated Rayleigh distribution under type II progressive censored samples. Estimation of reliability and hazard functions is also considered. Maximum likelihood estimators are obtained using the Expectation–Maximization (EM) algorithm. Further, we obtain expected Fisher information matrix using the missing value principle. Bayes estimators are derived under squared error and linex loss functions. We have used Lindley, and Tiernery and Kadane methods to compute these estimates. In addition, Bayes estimators are computed using importance sampling scheme as well. Samples generated from this scheme are further utilized for constructing highest posterior density intervals for unknown parameters. For comparison purposes asymptotic intervals are also obtained. A numerical comparison is made between proposed estimators using simulations and observations are given. A real-life data set is analyzed for illustrative purposes.

Keywords:

• Bayes estimator
• HPD interval
• importance sampling scheme
• Lindley method
• maximum likelihood estimator
• progressive type II censoring
• Tierney and Kadane method

MSC:

• 62F10
• 62F15
• 62N01

Acknowledgements

The authors are thankful to the Editor and anonymous referees for their valuable suggestions which have led to much improvements in the manuscript.