Re: Notebook for Borel-Tanner Distribution

• To: mathgroup at smc.vnet.net
• Subject: [mg62661] Re: Notebook for Borel-Tanner Distribution
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 30 Nov 2005 05:40:35 -0500 (EST)
• Organization: The University of Western Australia
• References: <dl6pje\$8uq\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <dl6pje\$8uq\$1 at smc.vnet.net>,
"kristoph" <kristophs.post at web.de> wrote:

> Has anybody a notebook for caculating the Borel-Tanner distribution? I
> know there is something in the book of Michael Trott "The Mathematica
> Guide Book for Numerics" but I do not want to spend that much money for
> a couple of pages.

I don't think that Michael will mind me forwarding his code for the
Borel-Tanner distribution:

u[c_] := 1 - 1/c NSum[k^(k - 2)/k! (c Exp[-c])^k, {k, Infinity},
Method -> Fit, VerifyConvergence -> False]

A plot of this function (and its derivative) is most interesting. u[c]
has the value c/2 for 0 <= c <= 1. For example,

Off[SequenceLimit::seqlim];
Plot[2/c u[c], {c,-1,8}, PlotRange->{All, {0,1.1}}]

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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