Re: Skellam distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg102191] Re: [mg102152] Skellam distribution*From*: Darren Glosemeyer <darreng at wolfram.com>*Date*: Sat, 1 Aug 2009 03:57:44 -0400 (EDT)*References*: <200907310952.FAA19191@smc.vnet.net>

Peter Breitfeld wrote: > Is there an implementation of the Skellam distribution? If not, how > would you implement a CDF for this distribution? > > I do not know if anyone has written Mathematica code for the Skellam distribution. The cdf can be computed for numerical values using NSum. In[1]:= skellamCDF[m1_?NonNegative, m2_?NonNegative, y_?NumericQ] := NSum[Exp[-m1 - m2] (m1/m2)^(k/2) BesselI[k, 2 Sqrt[m1 m2]], {k, -Infinity, Floor[y]}] In[2]:= Table[skellamCDF[2.5, 3, i], {i, -10, 10}] Out[2]= {0.000172756, 0.000631067, 0.00211362, 0.00644901, 0.0178004, 0.044116, 0.0974347, 0.190456, > 0.32791, 0.497063, 0.667993, 0.808954, 0.904408, 0.95824, 0.983953, 0.994528, 0.99833, 0.99954, > 0.999885, 0.999974, 0.999994} In[3]:= Plot[skellamCDF[2.5, 3, i], {i, -10, 10}] Out[3]= -Graphics- Darren Glosemeyer Wolfram Research