Dispersion Parameter

To describe the stochastic nature of an outcome variable, environmetricians use probability distributions. A crucial feature of many simple probability models is that structural relationships may be required between the population mean and other components of the model. Many environmental sampling and experimental settings occur, however, where such a mean/variance structure is too restrictive: the data often exhibit variation larger than or, in some instances, smaller than that required under these simpler models. Such occurrences are known collectively as overdispersion or underdispersion, respectively. We quantify the extent of the over/underdispersion by dedicating a model parameter to it in the variance term. The resulting dispersion parameter can be used to identify, study, test, or otherwise account for the excess variation. This entry reviews statistical aspects of modeling and estimation for such dispersion parameters.