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?