Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the "base" and the "exponent" . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases:
Exponential dispersion model
In probability and statistics, the class of exponential dispersion models (EDM) is a set of probability distributions that represents a generalisation of the natural exponential family. 
Exponential dispersion models play an important role in statistical theory, in particular in generalized linear models because they have a special structure which enables deductions to be made about appropriate statistical inference. 
There are two versions to formulate an exponential disperson model.
In the univariate case, a real-valued random variable formula_1 belongs to the additive exponential dispersion model with canonical parameter formula_2 and index parameter formula_3, formula_4, if its probability density function can be written as