Maximum Likelihood Estimation in the Bivariate Binomial (0,1) Distribution:Application TO 2×2 Tables |
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| Authors: | M A Hamdan E O Martinson |
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| Institution: | Virginia Polytechnic Institute and American University of Beirut;Virginia Polytechnic Institute |
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| Abstract: | We consider a 2×2 contingency table, with dichotomized qualitative characters (A,A) and (B,B), as a sample of size n drawn from a bivariate binomial (0,1) distribution. Maximum likelihood estimates p?1p?2 and p? are derived for the parameters of the two marginals p1p2 and the coefficient of correlation. It is found that p? is identical to Pearson's (1904)?=(χ2/n)½, where ?2 is Pearson's usual chi-square for the 2×2 table. The asymptotic variance-covariance matrix of p?lp?2and p is also derived. |
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