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The Exact Asymptotic Distribution Function of Watson's UN-Squared for Testing Goodness-of-Fit With Circular Discrete Data

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Abstract

We show that the full asymptotic distribution for Watson’s statistic, modified for discrete data, can be computed by standard methods. Previous approximate percentiles for the uniform multinomial case are found to be accurate. More extensive percentiles are presented for this distribution, and for the distribution associated with “Benford’s Law”.

Suggested Citation

  • David E. A. Giles, 2006. "The Exact Asymptotic Distribution Function of Watson's UN-Squared for Testing Goodness-of-Fit With Circular Discrete Data," Econometrics Working Papers 0607, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0607
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0607.pdf
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    References listed on IDEAS

    as
    1. David Giles, 2007. "Benford's law and naturally occurring prices in certain ebaY auctions," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 157-161.
    2. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    3. Canessa, Enrique, 2003. "Theory of analogous force on number sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 44-52.
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    More about this item

    Keywords

    Distributions on the Circle; Goodness-of-fit; Watson's UN-squared; Discrete data; Benford's Law;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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