[jira] [Commented] (STATISTICS-25) T Distribution Inverse Cumulative Probability Function gives the Wrong Answer

["Gilles Sadowski (Jira)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/STATISTICS-25?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17220092#comment-17220092 ] 

Gilles Sadowski commented on STATISTICS-25:
-------------------------------------------

I confirm that the equivalent code in [Commons Statistics|https://gitbox.apache.org/repos/asf?p=commons-statistics.git;a=blob;f=commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/TDistribution.java;h=5f74ff50a5077135f9ecca268f3a782a132be176;hb=HEAD] exhibits the same behaviour as {{Commons Math}} (used in the provided example).                        

The cause is plain limitation of {{double}}-precision in the [computation|https://gitbox.apache.org/repos/asf?p=commons-statistics.git;a=blob;f=commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/TDistribution.java;h=5f74ff50a5077135f9ecca268f3a782a132be176;hb=HEAD#l97] of   
{noformat}
degreesOfFreedom / (degreesOfFreedom + (x * x)
{noformat}
When {{degreesOfFreedom}} grows very large, the value is 1, whatever {{x}}.

Could you please provide the equivalent code from one of those other libraries, so that we can figure out how they work around this issue?


> T Distribution Inverse Cumulative Probability Function gives the Wrong Answer
> -----------------------------------------------------------------------------
>
>                 Key: STATISTICS-25
>                 URL: https://issues.apache.org/jira/browse/STATISTICS-25
>             Project: Apache Commons Statistics
>          Issue Type: Bug
>            Reporter: Andreas Stefik
>            Priority: Major
>
> Hi There,
> Given code like this:
>  
> import org.apache.commons.math3.analysis.UnivariateFunction;
> import org.apache.commons.math3.analysis.solvers.BrentSolver;
> import org.apache.commons.math3.distribution.TDistribution;
> public class Main {
>  public static void main(String[] args) {
>  double df = 1E38;
>  double t = 0.975;
>  TDistribution dist = new TDistribution(df);
>  
>  double prob = dist.inverseCumulativeProbability(1.0 - t);
>  
>  System.out.println("Prob: " + prob);
>  }
> }
>  
> It is possible I am misunderstanding, but that seems equivalent to:
>  
> scipy.stats.t.cdf(1.0 - 0.975, 1e38)
>  
> In Python. They give different answers. Python gives 0.509972518193, which seems correct, whereas Apache Commons gives  Prob: -6.462184036284304E-10. That's a huge difference.
> My hunch is that as you get closer to infinity it begins to fail, but I haven't checked carefully. For calls with much smaller degrees of freedom, you get answers that are basically the same as Python or online calculators.
>  



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