Generalized inverted exponential distribution under progressive first-failure censoring

Abstract

This article deals with progressive first-failure censoring, which is a generalization of progressive censoring. We derive maximum likelihood estimators of the unknown parameters and reliability characteristics of generalized inverted exponential distribution using progressive first-failure censored samples. The asymptotic confidence intervals and coverage probabilities for the parameters are obtained based on the observed Fisher's information matrix. Bayes estimators of the parameters and reliability characteristics under squared error loss function are obtained using the Lindley approximation and importance sampling methods. Also, highest posterior density credible intervals for the parameters are computed using importance sampling procedure. A Monte Carlo simulation study is conducted to analyse the performance of the estimators derived in the article. A real data set is discussed for illustration purposes. Finally, an optimal censoring scheme has been suggested using different optimality criteria.

Keywords:

• progressive first-failure censoring
• maximum likelihood estimation
• Bayes estimation
• Lindley approximation
• importance sampling
• optimum censoring scheme

Mathematics Subject Classification:

• Primary: 62N01
• 62N05
• Secondary: 62F10
• 62F15

Acknowledgements

The authors express their sincere thanks to the associate editor and the anonymous referee for their valuable comments and suggestions that greatly improved this article.

Disclosure statement

No potential conflict of interest was reported by the authors.