Levy heavy-tailed distribution (infinite moments with radical PDF and Erfc CDF)
LevyDistribution[μ, σ]
Mean[LevyDistribution[μ, σ]]
→ InfinityPDF[LevyDistribution[μ, σ], x]
→ Piecewise[{{(σ/(x - μ))^(3/2)/(E^(σ/(2*(x - μ)))*Sqrt[2*Pi]*σ), -μ + x > 0}}, 0]CDF[LevyDistribution[μ, σ], x]
→ Piecewise[{{Erfc[Sqrt[σ/(x - μ)]/Sqrt[2]], -μ + x > 0}}, 0]