Re: Skellam distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg102208] Re: [mg102152] Skellam distribution
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 1 Aug 2009 04:01:11 -0400 (EDT)
- Reply-to: hanlonr at cox.net
Clear[SkellamDistribution]; SkellamDistribution::usage = "SkellamDistribution[a1,a2] is the Skellam discrete probability \ distribution with parameters a1 and a2. \ http://en.wikipedia.org/wiki/Skellam_distribution";; SkellamDistribution /: PDF[ SkellamDistribution[a1_, a2_], k_] := Exp[-(a1 + a2)]*(a1/a2)^(k/2)* BesselI[k, 2 Sqrt[a1*a2]]; SkellamDistribution /: mgf[ SkellamDistribution[a1_, a2_], t_] := Exp[-(a1 + a2) + a1*Exp[t] + a2*Exp[-t]]; SkellamDistribution /: CharacteristicFunction[ SkellamDistribution[a1_, a2_], t_] := Exp[-(a1 + a2) + a1*Exp[I*t] + a2*Exp[-I*t]]; SkellamDistribution /: Moment[ SkellamDistribution[a1_, a2_], n_Integer] := Module[{t}, D[mgf[SkellamDistribution[a1, a2], t], {t, n}] /. t -> 0]; SkellamDistribution /: CDF[ SkellamDistribution[a1_, a2_], k_] := Sum[PDF[ SkellamDistribution[a1, a2], x], {x, -Infinity, k}]; SkellamDistribution /: Mean[ SkellamDistribution[a1_, a2_]] := (a1 - a2); SkellamDistribution /: Variance[ SkellamDistribution[a1_, a2_]] := (a1 + a2); SkellamDistribution /: StandardDeviation[ SkellamDistribution[a1_, a2_]] := Sqrt[a1 + a2]; Table[{n, Moment[SkellamDistribution[a1, a2], n]}, {n, 0, 2}] {{0, 1}, {1, a1 - a2}, {2, (a1 - a2)^2 + a1 + a2}} Bob Hanlon ---- Peter Breitfeld <phbrf at t-online.de> wrote: ============= Is there an implementation of the Skellam distribution? If not, how would you implement a CDF for this distribution? -- _________________________________________________________________ Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de