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https://issues.apache.org/jira/browse/MATH-1687?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=18076158#comment-18076158
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Gilles Sadowski commented on MATH-1687:
---------------------------------------
Version 3.6.1 of Commons Math is not supported anymore. Please check any issue
against the latest release.
In particular, the distributions are now implemented in another component:
[Commons
Statistics|https://commons.apache.org/proper/commons-statistics/commons-statistics-distribution/index.html]
(and corresponding [JIRA|https://issues.apache.org/jira/projects/STATISTICS]
project).
> FDistribution.inverseCumulativeProbability returns incorrect quantile (orders
> of magnitude error) for small degrees of freedom
> ------------------------------------------------------------------------------------------------------------------------------
>
> Key: MATH-1687
> URL: https://issues.apache.org/jira/browse/MATH-1687
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.6.1
> Environment: - OS: Windows 10 x64
> - Java version: JDK 17
> - Apache Commons Math: 3.6.1
> Reporter: 尹茂椿萱
> Priority: Major
>
> Description
> The method FDistribution.inverseCumulativeProbability(p) returns a value that
> does not satisfy the expected definition of a quantile.
> Specifically, the returned value is not the smallest x such that CDF（x） >= p,
> and is in fact several orders of magnitude larger than the correct solution.
> —
> Reproducible Example
> double numeratorDf = 0.10006;
> double denominatorDf = 1.51904;
> FDistribution dist = new FDistribution(numeratorDf, denominatorDf);
> double p = 0.16038;
> double x = dist.inverseCumulativeProbability(p);
> System.out.println("x = " + x);
> System.out.println("CDF（x） = " + dist.cumulativeProbability（x）);
> double x2 = x - 1e-9;
> System.out.println("CDF(x - 1e-9) = " + dist.cumulativeProbability(x2));
> // Scan for smaller valid x
> int steps = 1000000;
> double max = 1e-8;
> for (int i = 0; i < steps; i++) {
> double testX = i * (max / steps);
> double cdf = dist.cumulativeProbability(testX);
> if (cdf > p)
> { System.out.println("First x where CDF > p: " + testX + ", CDF=" +
> cdf); break; }
> }
> —
> Observed Behavior
> - inverseCumulativeProbability(p) returns:
> x ≈ 1.35e-9
> - CDF（x） ≈ 0.3069, which is significantly larger than p = 0.16038
> - A much smaller value exists:
> x ≈ 3.13e-15
> CDF（x） ≈ 0.16038
> —
> Expected Behavior
> The method should return a value x such that:
> - CDF（x） ≈ p
> - or at least the smallest x such that CDF（x） >= p
> —
> Severity of the issue
> This is not a small numerical error.
> The returned value is several orders of magnitude larger than the correct
> solution region:
> - Returned x ≈ 1.35e-9
> - However, values as small as 1e-14 already satisfy CDF（x） > p
> This demonstrates that the correct solution lies far below the returned value.
> Additionally:
> - CDF(returned x) ≈ 0.3069
> - target p = 0.16038
> So the returned value corresponds to a probability almost twice as large as
> requested.
> This indicates that the root-finding algorithm fails to locate the correct
> region,
> rather than suffering from minor floating-point inaccuracies.
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