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MathGroup Archive 2001

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Re: Plotting a discrete probability distribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30550] Re: [mg30531] Plotting a discrete probability distribution
  • From: BobHanlon at aol.com
  • Date: Wed, 29 Aug 2001 01:39:55 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2001/8/28 5:47:35 AM, dot at dot.dot writes:

>This will sound strange, but I would like to plot values defined by the
>function for the Poisson Distribution PDF, but for values that are not
>integers, and therefore not strictly part of the PDF
>
>PDF[PoissonDistribution[3],x] returns the function in x as one would expect,
>namely
>
>3^x/(E^3   * x!)
>
>I can now substitute values for x using
>
>/. x->valueWanted
>
>and have the function evaluate at valueWanted, but
>Plot[ PDF[PoissonDistribution[3],x], {x, 0, 5}]
>does not produce anything.
>
>Ah, I've just seen that I can do it with Evaluate around the PDF, but
>(1) *why* do I need it, when I do not need it with NormalDistribution?
>(2) If I want to evaluate (plot) values in the extremities of the
>PoissonDistribution, how can I push the precision in this case beyond
>MachinePrecision so that I do not just get zero?

Needs["Statistics`DiscreteDistributions`"];
Needs["Graphics`Colors`"];

You are plotting the envelope of the PDF.  A discrete PDF is composed of 
impulses.

mu = 3;

Plot[Evaluate[
      PDF[PoissonDistribution[mu], x]], 
    {x, -0.25, 10.25}, 
    PlotStyle -> {Blue, AbsoluteDashing[{5, 5}]}, 
    Epilog -> {Red, 
        Table[Line[{{x, 0}, 
              {x, PDF[PoissonDistribution[mu], x]}}], 
          {x, 0, 10}]}, 
    Frame -> True, Axes -> False, 
    FrameLabel -> {"\nx", "PDF\n"}, 
    PlotLabel -> "Poisson Distribution (mu = " <> 
        ToString[mu] <> ")", 
    ImageSize -> 400];

Plot[Evaluate[
      PDF[PoissonDistribution[mu], x]], 
    {x, 7.85, 12.15}, 
    PlotStyle -> {Blue, AbsoluteDashing[{5, 5}]}, 
    Epilog -> {Red, 
        Table[Line[{{x, 0}, 
              {x, PDF[PoissonDistribution[mu], x]}}], 
          {x, 8, 12}]}, 
    Frame -> True, Axes -> False, 
    FrameLabel -> {"\nx", "PDF\n"}, 
    PlotLabel -> "Poisson Distribution (mu = " <> 
        ToString[mu] <> ")", 
    ImageSize -> 400];


Bob Hanlon
Chantilly, VA  USA


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