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MathGroup Archive 2005

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Re: Notebook for Borel-Tanner Distribution

  • To: mathgroup at
  • Subject: [mg62661] Re: Notebook for Borel-Tanner Distribution
  • From: Paul Abbott <paul at>
  • Date: Wed, 30 Nov 2005 05:40:35 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <dl6pje$8uq$>
  • Sender: owner-wri-mathgroup at

In article <dl6pje$8uq$1 at>,
 "kristoph" < at> 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, 

  Plot[2/c u[c], {c,-1,8}, PlotRange->{All, {0,1.1}}]


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)    

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