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Characteristics of a TransformedDistribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128734] Characteristics of a TransformedDistribution
  • From: leigh pascoe <leigh at evry.inserm.fr>
  • Date: Wed, 21 Nov 2012 19:50:55 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • Delivered-to: l-mathgroup@wolfram.com
  • Delivered-to: mathgroup-newout@smc.vnet.net
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Could someone please help me to plot a transformed distribution?

Assuming we have 2 independent random variables, x1 and x2, distributed
as Binomial[n,p],

We would like to plot the pdf of the distribution of the random variable

    var=x1(1-x2)/x2(1-x1)

for various values of N (large) and p. This is a discrete distribution
with n2 possible values.

I have tried this numerous times, but always encounter either a syntax
error or a calculation that times out, even for small values of n.

I have defined the transformed distribution as follows.

or[n_, p_] :=
 TransformedDistribution[(y1/(n - y1))/(y2/(n -
       y2)), {y1 \[Distributed] BinomialDistribution[n, p],
   y2 \[Distributed] BinomialDistribution[n, p]}]

but have been unsuccessful trying to plot it, or determine its PDF, CDF,
Mean, Variance etc.

Any suggestions appreciated.

LP





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