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