Rice distribution (Bessel PDF and MarcumQ CDF and factored moments)
RiceDistribution[α, β]
RiceDistribution[m, α, β]
Mean[RiceDistribution[α, β]]
→ Sqrt[Pi/2]*β*LaguerreL[1/2, -1/2*α^2/β^2]PDF[RiceDistribution[α, β], x]
→ Piecewise[{{(E^((-x^2 - α^2)/(2*β^2))*x*BesselI[0, (x*α)/β^2])/β^2, x > 0}}, 0]CDF[RiceDistribution[α, β], x]
→ Piecewise[{{MarcumQ[1, α/β, 0, x/β], x > 0}}, 0]