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Modeling the Dependence between the Number of Trials and the Success Probability in Binary Trials
Author(s) -
Faddy M. J.,
Smith D. M.
Publication year - 2005
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2005.00466.x
Subject(s) - poisson distribution , bivariate analysis , negative binomial distribution , poisson binomial distribution , count data , continuity correction , generalization , binomial distribution , binomial (polynomial) , statistics , mathematics , poisson regression , binary number , econometrics , beta binomial distribution , medicine , mathematical analysis , population , environmental health , arithmetic
Summary A model for binary trials based on a bivariate generalization of the Poisson process for both the number of successes and number of trials with the transition rates dependent on the accumulating numbers of successes and trials is used to reanalyze some recently published data of Zhu, Eickhoff, and Kaiser (2003, Biometrics 59, 955–961). This modeling admits alternative distributions for the numbers of trials and the numbers of successes conditional on the number of trials which generalize the Poisson and binomial distributions, without some of the restrictions apparent in the beta‐binomial‐Poisson mixed modeling of Zhu et al. (2003). Some quite marked differences between the results of this analysis and those described in Zhu et al. (2003) are apparent.