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Estimation of the Burr type III distribution with application in unified hybrid censored sample of fracture toughness

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  • Hanieh Panahi

Abstract

In this paper, the statistical inference of the unknown parameters of a Burr Type III (BIII) distribution based on the unified hybrid censored sample is studied. The maximum likelihood estimators of the unknown parameters are obtained using the Expectation–Maximization algorithm. It is observed that the Bayes estimators cannot be obtained in explicit forms, hence Lindley's approximation and the Markov Chain Monte Carlo (MCMC) technique are used to compute the Bayes estimators. Further the highest posterior density credible intervals of the unknown parameters based on the MCMC samples are provided. The new model selection test is developed in discriminating between two competing models under unified hybrid censoring scheme. Finally, the potentiality of the BIII distribution to analyze the real data is illustrated by using the fracture toughness data of the three different materials namely silicon nitride (Si3N4), Zirconium dioxide (ZrO2) and sialon (Si6−xAlxOxN8−x). It is observed that for the present data sets, the BIII distribution has the better fit than the Weibull distribution which is frequently used in the fracture toughness data analysis.

Suggested Citation

  • Hanieh Panahi, 2017. "Estimation of the Burr type III distribution with application in unified hybrid censored sample of fracture toughness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(14), pages 2575-2592, October.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:14:p:2575-2592
    DOI: 10.1080/02664763.2016.1258549
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    Cited by:

    1. Hanieh Panahi, 2019. "Estimation for the parameters of the Burr Type XII distribution under doubly censored sample with application to microfluidics data," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(4), pages 510-518, August.

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