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Logistic or not Logistic?

Author

Listed:
  • James S. Allison
  • Bruno Ebner
  • Marius Smuts

Abstract

We propose a new class of goodness‐of‐fit tests for the logistic distribution based on a characterization related to the density approach in the context of Stein's method. This characterization‐based test is a first of its kind for the logistic distribution. The asymptotic null distribution of the test statistic is derived and it is shown that the test is consistent against fixed alternatives. The finite sample power performance of the newly proposed class of tests is compared to various existing tests by means of a Monte Carlo study. It is found that this new class of tests are especially powerful when the alternative distributions are heavy tailed, like Student's t and Cauchy, or for skew alternatives such as the log‐normal, gamma and chi‐square distributions.

Suggested Citation

  • James S. Allison & Bruno Ebner & Marius Smuts, 2023. "Logistic or not Logistic?," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(4), pages 429-443, November.
    • Handle: RePEc:bla:stanee:v:77:y:2023:i:4:p:429-443
    DOI: 10.1111/stan.12292
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    References listed on IDEAS

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    1. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
    2. Hadi Alizadeh Noughabi, 2022. "A New Goodness-of-Fit Test for the Logistic Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 303-319, May.
    3. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 456-501, June.
    4. Steffen Betsch & Bruno Ebner, 2020. "Testing normality via a distributional fixed point property in the Stein characterization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 105-138, March.
    5. Hadi Alizadeh Noughabi, 2017. "Gini index based goodness-of-fit test for the logistic distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 7114-7124, July.
    6. Marija Cuparić & Bojana Milošević, 2022. "New characterization-based exponentiality tests for randomly censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 461-487, June.
    7. T.W. Epps, 2005. "Tests for location-scale families based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 99-114, September.
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    Cited by:

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