The Altham–Poisson distribution. (October 2015)

• Record Type: Journal Article
• Authors: Leask, Kerry L; Haines, Linda M
• Is Part Of: Statistical modelling. Volume 15:Number 5(2015)
• Page Start: 476
• Page End: 497
• Publication Date: 2015-10
• Subjects: dose–response -- Multiplicative binomial -- overdispersion -- Wadley's problem; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X15571161
• Languages: English
• ISSNs: 1471-082X

Abstract

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 byn in the multiplicative binomial model, with a Poisson distribution and its suitability for overdispersed data from a Wadley's problem setting is explored.