Expansions of Discrete Distributions and Some Binomial Applications

摘要

Charlier type B expansions are reviewed. For a unified treatment, symbolic andoperator notations are used. Special cases of such expansions have been suggested in the literature, to model dependency or extra-binomial variations. In the binomial case, there are various ways in which the distribution can be modified to accomodate a dependency structure. A case in point is the Altham distribution. A context in which the assumption of independent binary events, as required for the binomial distribution, is particularly unrealistic in small group decision making. It is shown that with pairwise dependency as modeled by Altham's distribution, we are not assured monotonicity for simple majority rule.