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Maximum Likelihood Estimation in the Bivariate Binomial (0,1) Distribution:Application TO 2×2 Tables
Author(s) -
Hamdan M. A.,
Martinson E. O.
Publication year - 1971
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1971.tb01255.x
Subject(s) - contingency table , mathematics , statistics , bivariate analysis , negative binomial distribution , pearson product moment correlation coefficient , covariance matrix , binomial distribution , multivariate normal distribution , table (database) , binomial coefficient , maximum likelihood , combinatorics , multivariate statistics , poisson distribution , computer science , data mining
Summary 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 p̂ 1 p̂ 2 and p̂ are derived for the parameters of the two marginals p 1 p 2 and the coefficient of correlation. It is found that p̂ is identical to Pearson's (1904)ϕ=(χ 2 /n)½, where ϕ 2 is Pearson's usual chi‐square for the 2×2 table. The asymptotic variance‐covariance matrix of p̂ l p̂ 2 and p is also derived.