**Build scan:**
https://gradle-enterprise.elastic.co/s/mvstrljdxml4o/tests/:x-pack:plugin:ml:test/org.elasticsearch.xpack.ml.aggs.changepoint.KDETests/testCdfAndSf


**Reproduction line:**
```
./gradlew ':x-pack:plugin:ml:test' --tests "org.elasticsearch.xpack.ml.aggs.changepoint.KDETests.testCdfAndSf" -Dtests.seed=30030C4BAA9A2205 -Dtests.locale=uk -Dtests.timezone=Asia/Gaza -Druntime.java=21
```

**Applicable branches:**
main

**Reproduces locally?:**
Yes

**Failure history:**
https://es-delivery-stats.elastic.dev/app/dashboards#/view/dcec9e60-72ac-11ee-8f39-55975ded9e63?_g=(refreshInterval:(pause:!t,value:60000),time:(from:now-7d%2Fd,to:now))&_a=(controlGroupInput:(chainingSystem:HIERARCHICAL,controlStyle:twoLine,ignoreParentSettings:(ignoreFilters:!f,ignoreQuery:!f,ignoreTimerange:!f,ignoreValidations:!t),panels:('0c0c9cb8-ccd2-45c6-9b13-96bac4abc542':(explicitInput:(dataViewId:fbbdc689-be23-4b3d-8057-aa402e9ed0c5,enhancements:(),fieldName:task.keyword,grow:!t,id:'0c0c9cb8-ccd2-45c6-9b13-96bac4abc542',searchTechnique:wildcard,selectedOptions:!(),singleSelect:!t,title:'Gradle%20Task',width:medium),grow:!t,order:0,type:optionsListControl,width:small),'144933da-5c1b-4257-a969-7f43455a7901':(explicitInput:(dataViewId:fbbdc689-be23-4b3d-8057-aa402e9ed0c5,enhancements:(),fieldName:name.keyword,grow:!t,id:'144933da-5c1b-4257-a969-7f43455a7901',searchTechnique:wildcard,selectedOptions:!('testCdfAndSf'),title:Test,width:medium),grow:!t,order:2,type:optionsListControl,width:medium),'4e6ad9d6-6fdc-4fcc-bf1a-aa6ca79e0850':(explicitInput:(dataViewId:fbbdc689-be23-4b3d-8057-aa402e9ed0c5,enhancements:(),fieldName:className.keyword,grow:!t,id:'4e6ad9d6-6fdc-4fcc-bf1a-aa6ca79e0850',searchTechnique:wildcard,selectedOptions:!('org.elasticsearch.xpack.ml.aggs.changepoint.KDETests'),title:Suite,width:medium),grow:!t,order:1,type:optionsListControl,width:medium))))


**Failure excerpt:**
```
java.lang.AssertionError: 
Expected: a numeric value within <0.05> of <0.5>
     but: <0.44848454753438083> differed by <0.0015154524656191687> more than delta <0.05>

  at __randomizedtesting.SeedInfo.seed([30030C4BAA9A2205:9A9B2CE2D5B336C4]:0)
  at org.hamcrest.MatcherAssert.assertThat(MatcherAssert.java:18)
  at org.junit.Assert.assertThat(Assert.java:956)
  at org.junit.Assert.assertThat(Assert.java:923)
  at org.elasticsearch.xpack.ml.aggs.changepoint.KDETests.testCdfAndSf(KDETests.java:43)
  at jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:103)
  at java.lang.reflect.Method.invoke(Method.java:580)
  at com.carrotsearch.randomizedtesting.RandomizedRunner.invoke(RandomizedRunner.java:1758)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$8.evaluate(RandomizedRunner.java:946)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$9.evaluate(RandomizedRunner.java:982)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$10.evaluate(RandomizedRunner.java:996)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at org.apache.lucene.tests.util.TestRuleSetupTeardownChained$1.evaluate(TestRuleSetupTeardownChained.java:48)
  at org.apache.lucene.tests.util.AbstractBeforeAfterRule$1.evaluate(AbstractBeforeAfterRule.java:43)
  at org.apache.lucene.tests.util.TestRuleThreadAndTestName$1.evaluate(TestRuleThreadAndTestName.java:45)
  at org.apache.lucene.tests.util.TestRuleIgnoreAfterMaxFailures$1.evaluate(TestRuleIgnoreAfterMaxFailures.java:60)
  at org.apache.lucene.tests.util.TestRuleMarkFailure$1.evaluate(TestRuleMarkFailure.java:44)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl$StatementRunner.run(ThreadLeakControl.java:390)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl.forkTimeoutingTask(ThreadLeakControl.java:843)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl$3.evaluate(ThreadLeakControl.java:490)
  at com.carrotsearch.randomizedtesting.RandomizedRunner.runSingleTest(RandomizedRunner.java:955)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$5.evaluate(RandomizedRunner.java:840)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$6.evaluate(RandomizedRunner.java:891)
  at com.carrotsearch.randomizedtesting.RandomizedRunner$7.evaluate(RandomizedRunner.java:902)
  at org.apache.lucene.tests.util.AbstractBeforeAfterRule$1.evaluate(AbstractBeforeAfterRule.java:43)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at org.apache.lucene.tests.util.TestRuleStoreClassName$1.evaluate(TestRuleStoreClassName.java:38)
  at com.carrotsearch.randomizedtesting.rules.NoShadowingOrOverridesOnMethodsRule$1.evaluate(NoShadowingOrOverridesOnMethodsRule.java:40)
  at com.carrotsearch.randomizedtesting.rules.NoShadowingOrOverridesOnMethodsRule$1.evaluate(NoShadowingOrOverridesOnMethodsRule.java:40)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at org.apache.lucene.tests.util.TestRuleAssertionsRequired$1.evaluate(TestRuleAssertionsRequired.java:53)
  at org.apache.lucene.tests.util.AbstractBeforeAfterRule$1.evaluate(AbstractBeforeAfterRule.java:43)
  at org.apache.lucene.tests.util.TestRuleMarkFailure$1.evaluate(TestRuleMarkFailure.java:44)
  at org.apache.lucene.tests.util.TestRuleIgnoreAfterMaxFailures$1.evaluate(TestRuleIgnoreAfterMaxFailures.java:60)
  at org.apache.lucene.tests.util.TestRuleIgnoreTestSuites$1.evaluate(TestRuleIgnoreTestSuites.java:47)
  at com.carrotsearch.randomizedtesting.rules.StatementAdapter.evaluate(StatementAdapter.java:36)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl$StatementRunner.run(ThreadLeakControl.java:390)
  at com.carrotsearch.randomizedtesting.ThreadLeakControl.lambda$forkTimeoutingTask$0(ThreadLeakControl.java:850)
  at java.lang.Thread.run(Thread.java:1583)

```
x-pack/plugin/ml/src/test/java/org/elasticsearch/xpack/ml/aggs/changepoint/KDETests.java
assertThat(kde.cdf(1000.0).value(), closeTo(1.0, 1e-10));
        assertThat(kde.sf(1000.0).value(), closeTo(0.0, 1e-10));
        assertThat(kde.sf(-1000.0).value(), closeTo(1.0, 1e-10));
        
        {
            double median = kde.data()[kde.size() / 2];
            KDE.ValueAndMagnitude cdf = kde.cdf(median);
            KDE.ValueAndMagnitude sf = kde.sf(median);
            assertThat(cdf.value(), closeTo(0.5, 0.05));
            assertThat(sf.value(), closeTo(0.5, 0.05));
        }
        
        for (int i = 0; i < 100; i++) {
            double x = randomDoubleBetween(-10.0, 110.0, true);
            KDE.ValueAndMagnitude cdf = kde.cdf(x);
            KDE.ValueAndMagnitude sf = kde.sf(x);
            assertThat(cdf.value() + sf.value(), closeTo(1.0, 1e-4));
        }
    }
    public void testSignificanceForUnderflow() {
        KDE kde = new KDE(new double[] { 1.0, 2.0, 3.0, 4.0, 5.0 }, 1.06);
        KDE.ValueAndMagnitude cdf = kde.cdf(-1000.0);
        KDE.ValueAndMagnitude sf = kde.sf(1000.0);
        assertThat(cdf.value(), equalTo(0.0));
        assertThat(sf.value(), equalTo(0.0));
        
        assertThat(cdf.isMoreSignificant(sf), equalTo(true));
    }
}