Exponential Families

Abstract

Suppose the data is a random sample from some parametric brand name distribution with parameters \(\boldsymbol{\theta }\). This brand name distribution comes from a family of distributions parameterized by \(\boldsymbol{\theta } \in \varTheta\). Each different value of \(\boldsymbol{\theta }\) in the parameter space Θ gives a distribution that is a member of the family of distributions. Often the brand name family of distributions is from an exponential family.