# 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 their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of 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 and identically distributed random variables. In place of and the names of the corresponding distributions and their parameters have been indicated.

## Discrete distributions

## Continuous distributions

- where is a random sample from and

## See also

- Infinite divisibility (probability)
- Stable distribution
- Product distribution
- Not to be confused with: Mixture distribution
- Sum of normally distributed random variables

## References

- Hogg, Robert V.; McKean, Joseph W.; Craig, Allen T. (2004).
*Introduction to mathematical statistics*(6th ed.). Upper Saddle River, New Jersey: Prentice Hall. p. 692. ISBN 978-0-13-008507-8. MR 467974.

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