Just as the normal distribution is the maximum information entropy distribution for fixed values of the first moment E ⁡ ⁡ ( X ) and second moment E ⁡ ⁡ ( X 2 ) (with the fixed zeroth moment E ⁡ ⁡ ( X 0 ) = 1 corresponding to the normalization condition), the q -Gaussian distribution is the maximum Tsallis entropy distribution for fixed values of these three moments.