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Defining a Discrete Probability Distribution using ProbabilityDistribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122503] Defining a Discrete Probability Distribution using ProbabilityDistribution
  • From: Jonathan Foley <jonefoley at gmail.com>
  • Date: Sun, 30 Oct 2011 04:23:09 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com


I'm trying to use ProbabilityDistribution (http://
reference.wolfram.com/mathematica/ref/ProbabilityDistribution.html) to
define a discrete probability distribution given a pdf. The problem is
I can't get it to actually be discrete:

In: twostatedist =
  ProbabilityDistribution[(Gamma[
       a/d + N]/(Gamma[N + 1]*Gamma[a/d + b/d + N])*(Gamma[a/d + b/d]/
       Gamma[a/d]) (c/d)^N*
     Hypergeometric1F1[a/d + N, a/d + b/d + N, -c/d]), {N, 0,
    Infinity, 1}, Assumptions -> {N \[Element] Integers && N >= 0}];
params = {a -> 0.3, b -> 60/25, c -> 60, d -> 0.2};
PDF[twostatedist /. params, 0.5]

Out: 0.00976739


This should yield a probability of 0 but it doesn't. Based on the
documentation for a discrete distribution you are supposed to use the
form ProbabilityDistribution[pdf,{x,xmin,xmax,dx}]. It is not
explained what dx is, but I assumed this was the step size, so I set
it to 1. I further tried to enforce discreteness by using Assumptions,
but this doesn't appear to work.

Does anyone know how to do this?



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