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Testing for discontinuity or type of distribution

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  • Garrod, Neil
  • Pirkovic, Sonja Ratej
  • Valentincic, Aljosa

Abstract

In this paper, we propose a simple test for the continuity of a distribution function or of the type of distribution. The main advantage of our test in comparison to others, as used in earnings-management studies, for example, is that no assumptions regarding the underlying distribution function are necessary. Nonetheless, by use of the Chebyshev inequality we are able to define the upper limit of probabilities of test values. Results of Monte Carlo simulations indicate the robustness of the test in that the hypothesis of continuity for distribution functions with jumps is rejected whilst for continuous distributions it is not rejected. We also show that the test appropriately rejects/does not reject hypotheses regarding the type of distribution that a set of data follows. The test is particularly reliable for samples of more than 5000 observations. Applications employing such tests, for example in the earnings-management literature, typically exceed this threshold.

Suggested Citation

  • Garrod, Neil & Pirkovic, Sonja Ratej & Valentincic, Aljosa, 2006. "Testing for discontinuity or type of distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(1), pages 9-15.
    • Handle: RePEc:eee:matcom:v:71:y:2006:i:1:p:9-15
    DOI: 10.1016/j.matcom.2005.09.002
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    References listed on IDEAS

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    1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    2. Degeorge, Francois & Patel, Jayendu & Zeckhauser, Richard, 1999. "Earnings Management to Exceed Thresholds," The Journal of Business, University of Chicago Press, vol. 72(1), pages 1-33, January.
    3. Takeuchi, Yoshiyuki, 2004. "On a statistical method to detect discontinuity in the distribution function of reported earnings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(1), pages 103-111.
    4. Zhang, Jin & Wu, Yuehua, 2005. "Likelihood-ratio tests for normality," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 709-721, June.
    5. Burgstahler, David & Dichev, Ilia, 1997. "Earnings management to avoid earnings decreases and losses," Journal of Accounting and Economics, Elsevier, vol. 24(1), pages 99-126, December.
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    Cited by:

    1. Li, Shaomin & Selover, David D. & Stein, Michael, 2011. ""Keep silent and make money": Institutional patterns of earnings management in China," Journal of Asian Economics, Elsevier, vol. 22(5), pages 369-382, October.
    2. Cho, Myojung & Hah, Young D. & Kim, Oliver, 2011. "Optimistic bias in management forecasts by Japanese firms to avoid forecasting losses," The International Journal of Accounting, Elsevier, vol. 46(1), pages 79-101, March.

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