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A characterization and a class of omnibus tests for the exponential distribution based on the empirical characteristic function

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The characteristic function φ(t) of an exponentially distributed random variable is characterized by having its squared modulus identically equal to the real part of φ(t). We study the behavior of a class of consistent tests for exponentiality based on a weighted integral involving the empirical counterparts of these quantities, corresponding to suitably rescaled data. Bibliography: 25 titles.

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References

  1. M. V. Alba, D. Barrera, and M. D. Jiménez, “A homogeneity test based on empirical characteristics functional,” Comput. Statist., 16, 255–270 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Baringhaus, N. Gürtler, and N. Henze, “Weighted integral test statistics and components of smooth tests of fit,” Austral. New Zeal. J. Statist., 42, 179–192 (2000).

    Article  Google Scholar 

  3. K. Bury, Statistical Distributions in Engineering, Cambridge Univ. Press (1999).

  4. T. W. Epps, “Limiting behavior of the ICF test for normality under Gram-Charlier alternatives,” Statist. Probab. Lett., 42, 175–184 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  5. N. Gürtler and N. Henze, “Goodness-of-fit tests for the Cauchy distribution based on the empirical characteristic function,” Ann. Inst. Statist. Math., 52, 267–286 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  6. N. Henze, B. Klar, and S. G. Meintanis, “Invariant tests for symmetry about an unspecified point based on the empirical characteristics function,” J. Multivar. Anal., 87, 275–297 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  7. N. Henze and S. G. Meintanis, “Goodness-of-fit tests based on a new characterization of the exponential distribution,” Commun. Statist. Theor. Meth., 31, 1479–1497 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  8. N. Henze and S. G. Meintanis, "Tests of fit for exponentiality based on the empirical Laplace transform," Statistics, 36, 147–161 (2002).

    MATH  MathSciNet  Google Scholar 

  9. N. Henze and S. G. Meintanis, "Recent and classical tests for exponentiality: A partial review with comparisons," Metrika, 61, 29–45 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  10. N. Husskovaa and S. Meintanis, "Change point analysis based on empirical characteristic functions," Metrika, 63, 145–168 (2006).

    Article  MathSciNet  Google Scholar 

  11. M. Husskovaa and S. Meintanis," Change point analysis based on ranks of empirical characteristic functions," Sequential Anal., 25, 1–16 (2006).

    Google Scholar 

  12. A. Kankainen and N. G. Ushakov," A consistent modification of a test for independence based on the empirical characteristic function," J. Math. Sci., 89, 1486–1494 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  13. B. Klar and S. Meintanis, "Tests for normal mixtures based on the empirical characteristic function," Comput. Statist. Dat. Anal., 9, 227–242 (2005).

    Article  MathSciNet  Google Scholar 

  14. I. A. Koutrouvelis and S. G. Meintanis, "Testing for stability based on the empirical characteristic function with applications to financial data," J. Statist. Comput. Simul., 6, 275–300 (1999).

    Article  Google Scholar 

  15. M. Matsui and A. Takemura, "Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE," Ann. Instit. Statist. Math., 57, 183–199 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  16. S. G. Meintanis, "A class of omnibus tests for the Laplace distribution based on the empirical characteristic function," Commun. Statist. Theor. Meth., 33, 925–948(2004).

    Article  MATH  MathSciNet  Google Scholar 

  17. S. G. Meintanis," Goodness-of-fit tests for the logistic distribution based on empirical transforms," Sankhya, 66, 304–324 (2004).

    MathSciNet  Google Scholar 

  18. S. G. Meintanis, "Consistent tests for symmetric stability with finite mean based on the empirical characteristic function," J. Statist. Plann. Inferen., 128, 373–380 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  19. S. G. Meintanis, "Permutation tests for homogeneity based on the empirical characteristic function," J. Nonparametr. Statist., 17, 583–592 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  20. S. G. Meintanis and G. Iliopoulos, "Characterizations of the exponential distribution based on certain properties of its characteristic function," Kybernetika, 39, 583–592 (2003).

    MathSciNet  Google Scholar 

  21. S. G. Meintanis and N. G. Ushakov, "Binned goodness-of-fit tests based on the empirical characteristic function," Statist. Probab. Lett., 69, 305–314 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  22. R. J. Serfing, Approximation Theorems of Mathematical Statistics, John Wiley and Sons, New York (1980).

    Book  Google Scholar 

  23. N. G. Ushakov, Selected Topics in Characteristic Functions, VSP, Utreht (1999).

    MATH  Google Scholar 

  24. A. W. van der Vaart and J. A. Wellner, Weak Convergence and Empirical Processes, Springer-Verlag, New York (1996).

    MATH  Google Scholar 

  25. L.-X. Zhu and G. Neuhaus, "Nonparametric Monte Carlo tests for multivariate distributions," Biometrika, 87, 919–928 (2000).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institut fur Stochastik, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    N. Henze

  2. National and Kapodistrian University of Athens, Athens, Greece

    S. G. Meintanis

Authors
  1. N. Henze
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  2. S. G. Meintanis
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Correspondence to N. Henze.

Additional information

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 368, 2009, pp. 268–281.

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Henze, N., Meintanis, S.G. A characterization and a class of omnibus tests for the exponential distribution based on the empirical characteristic function. J Math Sci 167, 588–595 (2010). https://doi.org/10.1007/s10958-010-9946-5

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  • DOI: https://doi.org/10.1007/s10958-010-9946-5

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