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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

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Listed:
  • Mahmood Kharrati-Kopaei

    (Shiraz University)

  • Ahad Malekzadeh

    (K.N. Toosi University of Technology)

Abstract

We consider the problem of providing the exact distribution of the likelihood ratio test (LRT) statistic for testing the homogeneity of scale parameters of $$ k \ge 2 $$ k ≥ 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.

Suggested Citation

  • Mahmood Kharrati-Kopaei & Ahad Malekzadeh, 2019. "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," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 409-427, May.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:4:d:10.1007_s00184-018-00704-3
    DOI: 10.1007/s00184-018-00704-3
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    References listed on IDEAS

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    1. Stehlík, Milan, 2006. "Exact likelihood ratio scale and homogeneity testing of some loss processes," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 19-26, January.
    2. Alvarez-Andrade, S. & Balakrishnan, N. & Bordes, L., 2007. "Homogeneity tests based on several progressively Type-II censored samples," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1195-1213, July.
    3. N. Balakrishnan & Donghoon Han & G. Iliopoulos, 2011. "Exact inference for progressively Type-I censored exponential failure data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 335-358, May.
    4. Sadooghi-Alvandi, Soltan Mohammad & Malekzadeh, Ahad, 2013. "A note on testing homogeneity of the scale parameters of several inverse Gaussian distributions," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1844-1848.
    5. Maurya, Vishal & Goyal, Anju & Gill, Amar Nath, 2011. "Simultaneous testing for the successive differences of exponential location parameters under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1507-1517, October.
    6. N. J. Hill & A. R. Padmanabhan & Madan L. Puri, 1988. "Adaptive Nonparametric Procedures and Applications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(2), pages 205-218, June.
    7. Robert J. Boik, 1993. "Null Distribution of a Statistic for Testing Sphericity and Additivity: A Jacobi Polynomial Expansion," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(3), pages 567-576, September.
    8. Conghua Cheng & Jinyuan Chen & Jianming Bai, 2013. "Exact inferences of the two-parameter exponential distribution and Pareto distribution with censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1464-1479, July.
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    Cited by:

    1. Ali Akbar Jafari & Javad Shaabani, 2020. "Comparing scale parameters in several gamma distributions with known shapes," Computational Statistics, Springer, vol. 35(4), pages 1927-1950, December.
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    3. Mahmood Kharrati-Kopaei, 2021. "On the exact distribution of the likelihood ratio test statistic for testing the homogeneity of the scale parameters of several inverse Gaussian distributions," Computational Statistics, Springer, vol. 36(2), pages 1123-1138, June.

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