List of convolutions of probability distributions
In probability theory, the probability distribution of the sum of two or more independent random variables is the Convolution of [probability distributions|convolution] of their individual distributions. The term is motivated by the fact that the probability [mass function] or probability [density function] of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively. Many well known distributions have simple convolutions. The following is a list of these convolutions. Each statement is of the form
where are independent random variables, and is the distribution that results from the convolution of. In place of and the names of the corresponding distributions and their parameters have been indicated.
Discrete distributions
*Continuous distributions
The following three statements are special cases of the above statement:- where is a random sample from and
*