Estimation for the generalized Fréchet distribution under progressive censoring scheme

Kousik Maiti and Suchandan Kayal ()
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Kousik Maiti: National Institute of Technology Rourkela
Suchandan Kayal: National Institute of Technology Rourkela

International Journal of System Assurance Engineering and Management, 2019, vol. 10, issue 5, No 28, 1276-1301

Abstract: 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; 62F15; 62N05; 62N01; 62F12; 62N02; 62M20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13198-019-00875-w

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