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Distribution-free goodness-of-fit tests for the Pareto distribution based on a characterization

Author

Listed:
  • James Allison

    (North-West University)

  • Bojana Milošević

    (University of Belgrade)

  • Marko Obradović

    (University of Belgrade)

  • Marius Smuts

    (North-West University)

Abstract

We propose three new classes of goodness-of-fit tests for the Pareto type I distribution based on a characterization. The asymptotic null distribution for the tests are derived and their Bahadur efficiencies are compared to the efficiencies of some of the existing tests. It is found that the new integral type test has superior local efficiencies amongst the new tests, and in general, has higher efficiencies than the competing tests considered. The finite-sample performance of the newly proposed tests is evaluated and compared to that of other existing tests by means of a Monte Carlo study. It is found that the new tests (especially the integral type tests) perform favourably compared to the other tests.

Suggested Citation

  • James Allison & Bojana Milošević & Marko Obradović & Marius Smuts, 2022. "Distribution-free goodness-of-fit tests for the Pareto distribution based on a characterization," Computational Statistics, Springer, vol. 37(1), pages 403-418, March.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:1:d:10.1007_s00180-021-01126-y
    DOI: 10.1007/s00180-021-01126-y
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    References listed on IDEAS

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    1. Mohamed E. Ghitany & Emilio Gómez-Déniz & Saralees Nadarajah, 2018. "A New Generalization of the Pareto Distribution and Its Application to Insurance Data," JRFM, MDPI, vol. 11(1), pages 1-14, February.
    2. Jovanović, Milan & Milošević, Bojana & Nikitin, Ya. Yu. & Obradović, Marko & Volkova, K. Yu., 2015. "Tests of exponentiality based on Arnold–Villasenor characterization and their efficiencies," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 100-113.
    3. George Tzavelas, 2019. "A characterization of the Pareto distribution based on the Fisher information for censored data under non-regularity conditions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 429-440, May.
    4. Ya. Nikitin, 2010. "Large deviations of U-empirical Kolmogorov–Smirnov tests and their efficiency," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 649-668.
    5. Yakov Y. Nikitin & Irina Peaucelle, 2004. "Efficiency and local optimality of nonparametric tests based on U- and V-statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 185-200.
    6. Brazauskas, Vytaras & Serfling, Robert, 2003. "Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 365-381, November.
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    Cited by:

    1. 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.
    2. Meintanis, S.G. & Milošević, B. & Jiménez–Gamero, M.D., 2024. "Goodness–of–fit tests based on the min–characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).

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