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On the Chi-Square Goodness-of-Fit Statistic for Bivariate Discrete Distributions

S. Loukas and C. D. Kemp
Journal of the Royal Statistical Society. Series D (The Statistician)
Vol. 35, No. 5 (1986), pp. 525-529
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2987967
Stable URL: http://www.jstor.org/stable/2987967
Page Count: 5
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On the Chi-Square Goodness-of-Fit Statistic for Bivariate Discrete Distributions
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Abstract

Assessing goodness-of-fit for bivariate discrete distributions, using the classical Pearson chi-squared statistic, is much less straightforward than in univariate situations due to the relatively large number of classes with low expectation and the two-based structure. In this paper three procedures for grouping into chi-squared classes are examined (one row-based, one column-based, one using ordered expected-frequencies). Approximate asymptotic power has been computed for each procedure, using two minimum-expected-frequency criteria (4 and 1), applied to a variety of bivariate Poisson and compound Poisson distributions. In the light of these comparisons, the 'ordered-frequencies' method is recommended as a simple systematic standard procedure. The choice of minimum group size had relatively little effect.

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