The Altham–Poisson distribution

The multiplicative binomial model was introduced as a generalization of the binomial distribution for modelling correlated binomial data. This distribution has not been extensively explored and is revisited in the present study. Some properties of the multiplicative binomial distribution, such as, expressions for the factorial moments and the information matrix, are investigated. The distribution is also extended to accommodate data arising from a Wadley's problem setting which is frequently encountered in dose–mortality studies and is one in which the number of organisms initially treated with a drug is unobserved. The Altham–Poisson distribution is introduced by modelling the unobserved initial number of organisms, as specified by (Formula presented.) in the multiplicative binomial model, with a Poisson distribution and its suitability for overdispersed data from a Wadley's problem setting is explored.