Goodness-of-Fit Tests Based on a Characterization of Logistic Distribution

  • Ya. Yu. NikitinEmail author
  • I. A. RagozinEmail author


The logistic family of distributions belongs to the class of important families in the theory of probability and mathematical statistics. However, the goodness-of-fit tests for the composite hypothesis of belonging to the logistic family with unknown location parameter against the general alternatives have not been sufficiently explored. We propose two new goodness-of-fit tests: the integral and the Kolmogorov-type, based on the recent characterization of the logistic family by Hua and Lin. Here we discuss asymptotic properties of new tests and calculate their Bahadur efficiency for common alternatives.


characterization of distributions logistic distribution asymptotic efficiency large deviations Kullback-Leibler information 


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  1. 1.
    N. Balakrishnan, Handbook of the Logistic Distribution (CRC, New York, 1991).Google Scholar
  2. 2.
    M. A. Stephens, “Tests of fit for the logistic distribution based on the empirical distribution function,” Biometrika 66, 591–595 (1979).CrossRefzbMATHGoogle Scholar
  3. 3.
    Y. Y. Nikitin, “Tests based on characterizations, and their efficiencies: A survey,” Acta Commentat. Univ. Tartuensis Math. 21, 3–24 (2017).MathSciNetGoogle Scholar
  4. 4.
    K. Yu. Volkova, “New tests for the logistic distribution based on the functionals of U-empirical process,” in Proc. 12th Int. Vilnius Conf. on Probability and Mathematical Statistics, Vilnius, Lithuania, July 2–6, 2018 (IMS, Vilnius, 2018), p. 297.Google Scholar
  5. 5.
    C.-Y. Hu and G. D. Lin, “Characterizations of the logistic and related distributions,” J. Math. Anal. Appl. 463, 79–92 (2018).MathSciNetCrossRefGoogle Scholar
  6. 6.
    J. Galambos, “Characterizations,” in N. Balakrishnan, Handbook of the Logistic Distribution (CRC, New York, 1991), pp. 169–188.Google Scholar
  7. 7.
    G. D. Lin and C. Y. Hu, “On characterizations of the logistic distribution,” J. Stat. Plann. Inference 138, 1147–1156 (2008).MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Ahsanullah, G. P. Yanev, and C. Onica, “Characterizations of logistic distribution through order statistics with independent exponential shifts,” Stochastics Qual. Control 27, 85–96 (2011).Google Scholar
  9. 9.
    V. S. Korolyuk and Y. V. Borovskich, Theory of U-Statistics (Springer-Verlag, Dordrecht, 2013).Google Scholar
  10. 10.
    R. R. Bahadur, Some Limit Theorems in Statistics (SIAM, Philadelphia, PA, 1971).zbMATHGoogle Scholar
  11. 11.
    R. R. Bahadur, “Stochastic comparison of tests,” Ann. Math. Stat. 31, 276–295 (1960).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Ya. Yu. Nikitin, Asymptotic Efficiency of Nonparametric Tests, 2nd ed. (Nauka, Moscow, 1995; Cambridge Univ. Press, Cambridge, England, 2009).Google Scholar
  13. 13.
    C. Ley and D. Paindaveine, “Le Cam optimal tests for symmetry against Ferreira and Steel’s general skewed distributions,” J. Nonparametric Stat. 21, 943–967 (2009).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Ya. Yu. Nikitin and K. Yu. Volkova, “Efficiency of exponentiality tests based on a special property of exponential distribution,” Math. Methods Stat. 25, 54–66 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Ya. Yu. Nikitin and E. V. Ponikarov, “Rough large deviation asymptotics of Chernoff type for von Mises functionals and U-statistics,” AMS Transl., Ser. 2 203, 107–146 (2001).zbMATHGoogle Scholar
  16. 16.
    Ya. Yu. Nikitin and I. Peaucelle, “Efficiency and local optimality of distribution-free tests based on U- and V-statistics,” Metron 62, 185–200 (2004).MathSciNetGoogle Scholar
  17. 17.
    Ya. Yu. Nikitin, “Large deviations of U-empirical Kolmogorov-Smirnov tests, and their efficiency,” J. Non-parametric Stat. 22, 649–668 (2010).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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