In [[statistics]], the '''variance function''' is a function relating the variance of a random quantity to the conditional mean of the random quantity. The '''variance function''' is a main ingredient in the [[generalized linear model]] framework and plays roles in [[Non-parametric statistics]] and [[Functional data analysis]] as well. Not to be confused with the '''[[[variance]]] of a function''', in parametric modelling, variance functions explicitly describe the relationship between the variance and the conditional mean of a random variable. For many well known distributions, the variance function represents the complete variance of a random variable under that distribution, but in fact, variance functions only express the part of the variance that is dependent on the mean. it only consists of the part of the variance that is dependent o of the variance of a random variable tha Not to be confused with '''the variance of a function', the ''' variance function''' is a function that describes the relationship between the mean and variance of a random variable. a distribution used in [[generalized linear models]] and other areas, as a function of the mean. allows for response variables that have error distribution models other than a [[normal distribution]]. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a '''link function''' and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
