Stable distribution with PDF/CDF for Cauchy and Normal special cases
StableDistribution[type, α, β, μ, σ]
Mean[StableDistribution[0, α, β, μ, σ]]
→ Piecewise[{{μ - β*σ*Tan[(Pi*α)/2], Inequality[2, GreaterEqual, α, Greater, 1]}}, Indeterminate]Mean[StableDistribution[1, α, β, μ, σ]]
→ Piecewise[{{μ, Inequality[2, GreaterEqual, α, Greater, 1]}}, Indeterminate]Variance[StableDistribution[0, α, β, μ, σ]]
→ Piecewise[{{2*σ^2, α == 2}}, Indeterminate]