Skellam distribution of the difference of two Poisson variables
SkellamDistribution[μ 1, μ 2]
Mean[SkellamDistribution[Subscript[μ, 1], Subscript[μ, 2]]]
→ Subscript[μ, 1] - Subscript[μ, 2]PDF[SkellamDistribution[Subscript[μ, 1], Subscript[μ, 2]], x]
→ E^(-Subscript[μ, 1] - Subscript[μ, 2])*BesselI[x, 2*Sqrt[Subscript[μ, 1]*Subscript[μ, 2]]]*(Subscript[μ, 1]/Subscript[μ, 2])^(x/2)Variance[SkellamDistribution[Subscript[μ, 1], Subscript[μ, 2]]]
→ Subscript[μ, 1] + Subscript[μ, 2]