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------- Additional Comments From [EMAIL PROTECTED]  2005-08-17 20:36 -------
I think we're witnessing the accumulation of numerical error.  The cumulative 
probability method uses the textbook definition for its computation: summing 
the point probabilities.  Each of these probabilities results in a small 
numerical error and the process of summing them just exacerbates the error.

In your case, X ~ hyper(2000, 500, 100) and P(X <= 50) there are 51 small 
errors that, when added together, cause the total sum to be over 1.0.  Also, 
the point probabilities the larger x values (30 - 50) are so small that they 
provide little value to the overall sum, just error.

I think we can address this problem by simply short-circuiting the summation 
whenever it goes above 1.0.  This will solve the problem of cumulative 
probablities greater than 1 and make the upper tail probabilties correct 
because, again in your case, P(X >= 50) is extremely close to zero.

What do others think?


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