Birnbaum-Saunders fatigue-life distribution (Mean Variance PDF and Erf CDF)
BirnbaumSaundersDistribution[α, λ]
Mean[BirnbaumSaundersDistribution[α, λ]]
→ (2 + α^2)/(2*λ)PDF[BirnbaumSaundersDistribution[α, λ], x]
→ Piecewise[{{(1 + x*λ)/(2*E^((-1 + x*λ)^2/(2*x*α^2*λ))*Sqrt[2*Pi]*α*Sqrt[x^3*λ]), x > 0}}, 0]CDF[BirnbaumSaundersDistribution[α, λ], x]
→ Piecewise[{{(1 + Erf[(-1 + x*λ)/(Sqrt[2]*α*Sqrt[x*λ])])/2, x > 0}}, 0]