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From: divergent.tseries@gmail.com
Newsgroups: comp.soft-sys.matlab
Subject: Re: Augmenting a sample from unbounded distribution, until no values
 are above or below threshold.
Date: Thu, 2 Aug 2012 07:29:02 -0700 (PDT)
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Can you give a little more about the problem.  I work regularly with data that naturally comes from  a Cauchy distribution and real world data do look outside the threshold of reason.  You need to be careful with some real world modelling that your "threshold of reason" is nature's threshold of reason.  Processes like cancer or the stock market have quite unreasonable values as sets become large.

However, if you do think you have a real stochastic boundary condition, and you don't mind a little bit of skew a solution is to do the following

Draw x from a Cauchy distribution subject to x<=Y where y is drawn from a Cauchy distribution whose center is to the right of the center for x.

It creates a distribution of x times (1-CDF(y)).  This allows the data to increase without bounds, but does create a right side stochastic budget constraint.  That constraint is your boundary of reason, but allows nature to be "unreasonable."

Its important to remember that just because you cannot divide by zero, this does not prevent nature from doing so.

Sorry I didn't post matlab code, but it is rusty.