尹茂椿萱 created MATH-1687:
--------------------------
Summary: 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
### 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.
---
### Additional Notes
This issue was originally observed in Apache Commons Math 3.6.1 and appears to
persist in Hipparchus.
--
This message was sent by Atlassian Jira
(v8.20.10#820010)
