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

```

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