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