Doctoral Degrees (Applied Mathematics)

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Wadley's problem with overdispersion.
(2009) Leask, Kerry Leigh.; Haines, Linda Margaret.; Matthews, Glenda Beverley.
Wadley’s problem frequently emerges in dosage-mortality data and is one in which the number of surviving organisms is observed but the number initially treated is unknown. Data in this setting are also often overdispersed, that is the variability within the data exceeds that described by the distribution modelling it. The aim of this thesis is to explore distributions that can accommodate overdispersion in a Wadley’s problem setting. Two methods are essentially considered. The first considers adapting the beta-binomial and multiplicative binomial models that are frequently used for overdispersed binomial-type data to a Wadley’s problem setting. The second strategy entails modelling Wadley’s problem with a distribution that is suitable for modelling overdispersed count data. Some of the distributions introduced can be used for modelling overdispersed count data as well as overdispersed doseresponse data from a Wadley context. These models are compared using goodness of fit tests, deviance and Akaike’s Information Criterion and their properties are explored.