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On the exact distribution of the likelihood ratio test for testing the homogeneity of scale parameters of several two-parameter exponential distributions: complete and censored samples

  • Mahmood Kharrati-KopaeiEmail author
  • Ahad Malekzadeh


We consider the problem of providing the exact distribution of the likelihood ratio test (LRT) statistic for testing the homogeneity of scale parameters of \( k \ge 2 \) two-parameter exponential distributions. To this end, we apply the Millen inverse transform and the Jacobi polynomial expansion to the moments of LRT statistic. We consider the problem when the data are either complete or censored under the different kinds of Type II censoring, such as the Type II right, progressively Type II right, and double Type II censoring schemes. We also discuss the exact null distribution of the LRT when the data are censored under the Type I censoring scheme.


Double Type II censoring Jacobi polynomial expansion Likelihood ratio test Millen inverse transform Progressive Type II censoring Type I censoring Two-parameter exponential 

Mathematics Subject Classification

62F03 62P30 62E15 



The authors would like to thank referees for their constructive comments. The first author would like to thank the Research Council of Shiraz University.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsShiraz UniversityShirazIran
  2. 2.Department of Computer Science and Statistics, Faculty of MathematicsK.N. Toosi University of TechnologyTehranIran

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