Bayesian Inference for Nadarajah-Haghighi Distribution Under Progressively Type-II Censored Data

Reza  Azimi; Mahdy  Esmailian

Authors

Reza Azimi Department of Statistics and Computer Sciences, University of Mohaghegh Ardabili, Ardabil, Iran
Mahdy Esmailian Department of Statistics and Computer Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

Keywords:

Maximum likelihood estimation, Bayes estimation, reliability function, progressively order statistics, hazard function

Abstract

In this article, the problem of estimating parameters, reliability function, and hazard function
of the Nadarajah-Haghighi distribution under progressively type-II censored samples are studied.
The maximum likelihood and Bayesian estimators under squared error, LINEX, and general entropy loss functions are derived for parameters and some survival time parameters namely reliability and hazard functions. We used Lindley’s approximation to obtain the Bayesian estimators. Asymptotic confidence intervals, for unknown parameters, are constructed using the observed Fisher information
matrix. A numerical example using the real data set is presented to illustrate the proposed methods. Monte Carlo simulation study is conducted to compare the performance of the estimators in terms of their mean square error. The Monte Carlo simulation analysis shows that in most cases, the Bayesian method have a better performance than the standard maximum likelihood method.

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