An exponential family is a collection of statistical distributions whose probability densities or mass functions can be written
![f(x|eta)=h(x)exp[eta^TT(x)-A(eta)].](/images/equations/ExponentialFamily/NumberedEquation1.svg) |
Here 
is the natural parameter, 
is a vector of sufficient statistics, and 
is the log-partition function that normalizes the distribution.
When differentiation under the integral is valid, the gradient and Hessian of 
give the expectation value
and covariance matrix of 
. The normal distribution,
Poisson distribution, binomial
distribution, and gamma distribution have
standard exponential-family forms, although the choice of parameterization and support
matters.
