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Bayesian inference on multiply sequential order statistics from heterogeneous exponential populations with GLR test for homogeneity

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  • Majid Hashempour
  • Mahdi Doostparast

Abstract

In this article, sequential order statistics (SOS) coming from heterogeneous exponential distributions are considered. Maximum likelihood and Bayesian estimates of parameters are derived on the basis of multiple SOS samples. Admissibility of the Bayes estimates are discussed and proved by the well-known Blyth’s lemma. Based on the available data, confidence intervals and highest posterior density credible sets are obtained. The generalized likelihood ratio (GLRT) and the Bayesian tests (under the “0 − K” loss function) are derived for testing homogeneity of the exponential populations. It is shown that the GLRT in this case is scale invariant. Some guidelines for deriving the uniformly most powerful scale-invariant test (if exists) are also given.

Suggested Citation

  • Majid Hashempour & Mahdi Doostparast, 2017. "Bayesian inference on multiply sequential order statistics from heterogeneous exponential populations with GLR test for homogeneity," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 8086-8100, August.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:16:p:8086-8100
    DOI: 10.1080/03610926.2016.1175625
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    Cited by:

    1. Tzong-Ru Tsai & Hua Xin & Chiun-How Kao, 2021. "Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions," Mathematics, MDPI, vol. 9(2), pages 1-21, January.
    2. Tzong-Ru Tsai & Yuhlong Lio & Hua Xin & Hoang Pham, 2021. "Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution," Mathematics, MDPI, vol. 9(8), pages 1-17, April.

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