Overdispersion at the Binomial and Multinomial Distribution

Abstract

Overdispersion is a widely discussed phenomenon in case of binomial and Poisson distributed data. We analysed multinomial data with varying multinomial parameters as a part of attribute gauge study. In this situation overdispersion is expected to occur. However in case of nonrepeated observations it is not present. We investigated and proved the ``lack´´ of overdispersion in case of binomial and multinomial variables if there are no repeated observations. The explanation is a ``compensation effect´´, which only occurs in case of binomial and multinomial variables and does not occur for Poisson distributed data.