Exponential family

Summary

An exponential family is a parametric family of probability distributions whose densities have the form $h(x) \exp\big(\sum_i \eta_i(\theta) T_i(x) - A(\theta)\big)$. Most standard distributions belong to one: normal, binomial, Poisson, gamma, beta and many more. The statistics $T_i$ are sufficient, and the structure makes estimation, testing and Bayesian updating explicit.