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https://issues.apache.org/jira/browse/MATH-718?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13253360#comment-13253360
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Thomas Neidhart commented on MATH-718:
--------------------------------------

The problem Christian described wrt the PascalDistribution is a simple integer 
overflow in the class itself:

{noformat}
    public double cumulativeProbability(int x) {
        double ret;
        if (x < 0) {
            ret = 0.0;
        } else {
            ret = Beta.regularizedBeta(probabilityOfSuccess,
                    numberOfSuccesses, x + 1);
        }
        return ret;
    }
{noformat}

when x = Integer.MAX_VALUE, adding 1 to it will result in an overflow. As the 
parameter of regularizedBeta is anyway a double, it should be cast to 
long/double before the addition.
                
> inverseCumulativeProbability of BinomialDistribution returns wrong value for 
> large trials.
> ------------------------------------------------------------------------------------------
>
>                 Key: MATH-718
>                 URL: https://issues.apache.org/jira/browse/MATH-718
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 2.2, 3.0
>            Reporter: Yuji Uchiyama
>            Assignee: Sébastien Brisard
>             Fix For: 3.1, 4.0
>
>
> The inverseCumulativeProbability method of the BinomialDistributionImpl class 
> returns wrong value for large trials.  Following code will be reproduce the 
> problem.
> {{System.out.println(new BinomialDistributionImpl(1000000, 
> 0.5).inverseCumulativeProbability(0.5));}}
> This returns 499525, though it should be 499999.
> I'm not sure how it should be fixed, but the cause is that the 
> cumulativeProbability method returns Infinity, not NaN.  As the result the 
> checkedCumulativeProbability method doesn't work as expected.

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