A Continuous Limit for the Contagious Binomial Distribution
A Continuous Limit for the Contagious Binomial Distribution
David Bruce Montgomery
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The parameter y measures the influence which the behavior of other individuals has over the behavior of any given individual. Coleman has utilized this form of the model to analyze the impact of inter- personal influence upon voting behavior in small groups. The motivation for developing the limiting form of (2) in this case is one of convenience rather than theoretical desirability. For moderately large groups, say groups having over twenty-five members, (2) will have N > 25 and will be comput...ationally inconvenient. The well tabled beta 'form will often prove to be a useful approximation in such cases. 5. Summary \ This paper has demonstrated that the beta distribution is the limit distribution of the "contagious" binomial. The structure of certain models which have the "contagious" binomial as the steady-state distribution was illustrated. FOOTNOTES 1. Coleman has coined the term "contagious binomial" to describe the distribution considered in this paper. 2. Coleman [3, p. 413] expressed the need for this limit but indicated that he had been unable to derive it.
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