Exponential Family Distributions

Many parametric distributions can be written in a similar form. This family of distributions is called the exponential family and has the form

\[p(x, \theta) = \frac{1}{Z(\theta)} h(x) \exp(\eta(\theta)^T T(x))\]

where \(\eta(\theta)\) are the natural parameters, \(T(x)\) are the sufficient statistics and \(Z(\theta)\) is a normalization constant.