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Following is a table of several exponential-family distributions in common use and the data they are typically used for, along with the canonical link functions and their inverses (sometimes referred to as the mean function, as done here).
{| class="wikitable
|+ Common distributions with typical uses and canonical link functions
! Distribution !! Support of distribution !! Typical uses !! Link name !! Link function, <math>\mathbf{X}\boldsymbol{\beta}=g(\mu)\,\!</math> !! Mean function
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