Tsallis q-Gaussian distribution
TsallisQGaussianDistribution[μ, β, q]
TsallisQGaussianDistribution[q]
Mean[TsallisQGaussianDistribution[μ, β, q]]
→ Piecewise[{{μ, q < 2}}, Indeterminate]Variance[TsallisQGaussianDistribution[μ, β, q]]
→ Piecewise[{{(2*β^2)/(5 - 3*q), q < 5/3}, {Infinity, Inequality[5/3, LessEqual, q, Less, 2]}}, Indeterminate]Plot[Table[PDF[TsallisQGaussianDistribution[0, 2, q], x], {q, {0, 1, 2}}]//Evaluate, {x, -4, 4}, Filling -> Axis]
→ -Graphics-