Exponential family
What is important to note, and what characterizes all exponential family variants, is that the parameter(s) and the observation variable(s) must factorize (can be separated into products each of which involves only one type of variable), either directly or within either part (the base or exponent) of an exponentiation operation. Generally, this means that all of the factors constituting the density or mass function must be of one of the following forms:
Cis (mathematics)
The notation is sometimes used to emphasize one method of viewing and dealing with a problem over another. The mathematics of trigonometry and exponentials are related but not exactly the same; exponential notation emphasizes the whole, whereas and notations emphasize the parts. This can be rhetorically useful to mathematicians and engineers when discussing this function, and further serve as a mnemonic (for ).