IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v77y2023i4p429-443.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12292
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12292?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Klar, B. & Lindner, F. & Meintanis, S.G., 2012. "Specification tests for the error distribution in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3587-3598.
    2. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    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. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.
    5. Meintanis, Simos G. & Iliopoulos, George, 2008. "Fourier methods for testing multivariate independence," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1884-1895, January.
    6. L. Ndwandwe & J. S. Allison & L. Santana & I. J. H. Visagie, 2023. "Testing for the Pareto type I distribution: a comparative study," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 215-256, August.
    7. Bruno Ebner & Norbert Henze, 2023. "On the eigenvalues associated with the limit null distribution of the Epps-Pulley test of normality," Statistical Papers, Springer, vol. 64(3), pages 739-752, June.
    8. Meintanis, Simos G. & Ushakov, Nikolai G., 2016. "Nonparametric probability weighted empirical characteristic function and applications," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 52-61.
    9. Simos G. Meintanis, 2020. "Comments on: Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 898-902, December.
    10. Simos Meintanis & Bojana Milošević & Marko Obradović & Mirjana Veljović, 2024. "Goodness‐of‐fit tests for the multivariate Student‐t distribution based on i.i.d. data, and for GARCH observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(2), pages 298-319, March.
    11. Jiménez-Gamero, M.D. & Alba-Fernández, M.V. & Jodrá, P. & Barranco-Chamorro, I., 2015. "An approximation to the null distribution of a class of Cramér–von Mises statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 258-272.
    12. Leucht, Anne & Neumann, Michael H., 2009. "Consistency of general bootstrap methods for degenerate U-type and V-type statistics," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1622-1633, September.
    13. 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.
    14. Natalie Neumeyer & Miguel A. Delgado & Lajos Horváth & Simos Meintanis & Emanuele Taufer & Lixing Zhu, 2021. "4th Workshop on Goodness‐of‐Fit, Change‐Point, and Related Problems, Trento, 2019," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 371-374, June.
    15. Juan Carlos Pardo-Fernández & María Dolores Jiménez-Gamero & Anouar El Ghouch, 2015. "A Non-parametric ANOVA-type Test for Regression Curves Based on Characteristic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 197-213, March.
    16. Sangyeol Lee & Simos G. Meintanis & Minyoung Jo, 2019. "Inferential procedures based on the integrated empirical characteristic function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 357-386, September.
    17. Christian Goldmann & Bernhard Klar & Simos Meintanis, 2015. "Data transformations and goodness-of-fit tests for type-II right censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 59-83, January.
    18. Jiménez-Gamero, M.D. & Alba-Fernández, V. & Muñoz-García, J. & Chalco-Cano, Y., 2009. "Goodness-of-fit tests based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3957-3971, October.
    19. Taufer, Emanuele & Leonenko, Nikolai & Bee, Marco, 2011. "Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2525-2539, August.
    20. Meintanis, Simos & Swanepoel, Jan, 2007. "Bootstrap goodness-of-fit tests with estimated parameters based on empirical transforms," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1004-1013, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:stanee:v:77:y:2023:i:4:p:429-443. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.