Rayleigh-lognormal compound distribution with closed-form Mean and Variance
SuzukiDistribution[μ, ν]
Mean[SuzukiDistribution[μ, ν]]
→ E^(μ + ν^2/2)*Sqrt[Pi/2]Variance[SuzukiDistribution[μ, ν]]
→ E^(2*μ + ν^2)*(-1/2*Pi + 2*E^ν^2)Plot[Table[PDF[SuzukiDistribution[2, ν], x], {ν, {1 / 2, 1, 5}}]//Evaluate, {x, 0, 10}, Filling -> Axis]
→ -Graphics-