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From "Sriram Natarajan (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-1185) Tail probability drops to zero beyond 10e-17 ?
Date Mon, 05 Jan 2015 15:45:35 GMT

    [ https://issues.apache.org/jira/browse/MATH-1185?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14264696#comment-14264696
] 

Sriram Natarajan commented on MATH-1185:
----------------------------------------

Thanks for the responses. I didn't think my post made it.

Stats packages like R, dcdf, Excel must be compromising with the precision in the representation
before the exponent  in order to at least represent the order of magnitude of the probability
(so a result upto Double.MinValue 2.2E-308 is feasible).  Isn't that what happens naturally?
f(130)/100 would be the same number of digits but the exponent would change to -18. Is the
decision made by R etc. in some way "wrong"?

http://en.wikipedia.org/wiki/Double-precision_floating-point_format does say that beyond 2^52
there are gaps in representable integers.  All that means is that the representation is not
exact. AFAIK, even 0.1 does not have an exact representation as a double.  Hence 0.1 + 0.2
isn't exactly 0.3.

> Tail probability drops to zero beyond 10e-17 ?
> ----------------------------------------------
>
>                 Key: MATH-1185
>                 URL: https://issues.apache.org/jira/browse/MATH-1185
>             Project: Commons Math
>          Issue Type: Wish
>    Affects Versions: 3.3, 3.4
>            Reporter: Sriram Natarajan
>            Priority: Minor
>
> This could be a  simple question, In which case I can expect a clarification. If this
is the wrong place to post such a question, let me know.
> OS: Windows 8.1, Java 1.8.0_25
> ChiSquaredDistribution chisq = new ChiSquaredDistribution(23)
> 1.0 - chisq.cumulativeProbability(130) is  1.1102230246251565E-16
> 1.0 - chisq.cumulativeProbability(131) is  0.0  
> Am pretty sure it is not a formatting issue.  Is there a reason why the tail drops to
zero at this point?



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