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Estimation for the generalized Fréchet distribution under progressive censoring scheme

  • Kousik Maiti
  • Suchandan KayalEmail author
Original Article
  • 283 Downloads

Abstract

This paper takes into account the estimation of the unknown model parameters and the reliability characteristics for a generalized Fréchet distribution under progressive type-II censored sample. Maximum likelihood estimates are obtained. We calculate asymptotic confidence intervals and also compare in terms of their coverage probabilities for the unknown parameters, and the reliability and hazard rate functions. Further, Bayes estimates are derived with respect to various balanced type symmetric as well as asymmetric loss functions. Note that it is impossible to get the estimates in closed-form. So, we adopt importance sampling method in computing the Bayes estimates. Furthermore, we consider one-sample and two-sample prediction problems under Bayesian framework. In this case, the appropriate predictive intervals are proposed. Monte Carlo simulations are performed to observe the performance of various estimates. Moreover, results from simulation studies indicating the performance of the proposed methods are included. Finally, a real dataset is considered and analyzed for the illustration of the inferential procedures studied in this paper.

Keywords

Progressive type-II censoring Maximum likelihood estimation Confidence intervals Balanced loss functions Bayesian estimation Importance sampling method Bayesian prediction Monte Carlo simulation 

Mathematics Subject Classification

62F15 62N05 62N01 62F12 62N02 62M20 

Notes

Acknowledgements

The authors would like to thank the Editor, Associate Editor and three anonymous reviewers for their valuable comments which have improved the presentation of this paper. One of the author Kousik Maiti thanks the Ministry of Human Resource Development (M.H.R.D.), Government of India for the financial assistantship received to carry out this research work. Suchandan Kayal gratefully acknowledges the partial financial support for this research work under a Grant MTR/2018/000350, SERB, India.

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Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of Technology RourkelaRourkelaIndia

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