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Chi-Squared Goodness of Fit Tests with Applications by M.S Nikulin, Vassilly Voinov, N. Balakrishnan

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Chapter 7

Applications of Modified Chi-Squared Tests

7.1 Poisson versus binomial: Appointment of judges to the US Supreme Court

The problem of discriminating between Poisson and binomial probability distributions is a very difficult one due to the close similarity between these two models; see Bol’shev (1963), Vu and Maller (1996), and Voinov and Voinov (2008, 2010). In this regard, we consider here a detailed statistical analysis of the number of US Supreme Court justices’ appointments from 1789 to 2004 (Voinov et al., 2010). Proposed modified chi-squared type tests, the likelihood ratio test of Vu and Maller (1996) and some other well-known tests are all examined with these data. The analysis shows that both simple Poisson and simple binomial ...

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