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Topic: Characteristics of a TransformedDistribution
Replies: 0

 leigh pascoe Posts: 30 Registered: 3/2/10
Characteristics of a TransformedDistribution
Posted: Nov 21, 2012 7:51 PM

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