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Statistical inference for α-series process with gamma distribution

Author

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  • Mahmut Kara
  • Halil Aydoğdu
  • Birdal Şenoğlu

Abstract

The explicit estimators of the parameters α, μ and σ2 are obtained by using the methodology known as modified maximum likelihood (MML) when the distribution of the first occurrence time of an event is assumed to be Weibull in series process. The efficiencies of the MML estimators are compared with the corresponding nonparametric (NP) estimators and it is shown that the proposed estimators have higher efficiencies than the NP estimators. In this study, we extend these results to the case, where the distribution of the first occurrence time is Gamma. It is another widely used and well-known distribution in reliability analysis. A real data set taken from the literature is analyzed at the end of the study for better understanding the methodology presented in this paper.

Suggested Citation

  • Mahmut Kara & Halil Aydoğdu & Birdal Şenoğlu, 2017. "Statistical inference for α-series process with gamma distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6727-6736, July.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:13:p:6727-6736
    DOI: 10.1080/03610926.2015.1134571
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