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List of convolutions of probability distributions

From Wikipedia, the free encyclopedia

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 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

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Continuous distributions

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The following three statements are special cases of the above statement:


  • [1]
  • [2]
  • [3]
  • where is a random sample from and

Mixed distributions:

See also

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References

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  1. ^ "VoigtDistribution". Wolfram Language Documentation. 2016 [2012]. Retrieved 2021-04-08.
  2. ^ "VarianceGammaDistribution". Wolfram Language Documentation (published 2016). 2012. Retrieved 2021-04-09.
  3. ^ Yanev, George P. (2020-12-15). "Exponential and Hypoexponential Distributions: Some Characterizations". Mathematics. 8 (12): 2207. arXiv:2012.08498. doi:10.3390/math8122207.

Sources

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