If a random variable X has a probability distribution (discrete case) or a probability density function (continuous case) that can be written in the form
where θ is a parameter and a, b, c, and d are known functions, then it is a member of the exponential family. The Poisson distribution, the binomial distribution, and the normal distribution are members of this family. If a(x)=x, then the distribution is in canonical form and b(θ) is a natural parameter of the distribution.
Subjects: Probability and Statistics.