[MATH-1240] Fix calculation of ksSum in KolmogorovSmirnovTest for zero input.

src/changes/changes.xml

@@ -54,6 +54,11 @@ If the output is not quite correct, check for invisible trailing spaces!
     </release>
 
     <release version="4.0" date="XXXX-XX-XX" description="">
+      <action dev="tn" type="fix" issue="MATH-1240"> <!-- backported to 3.6 -->
+        "KolmogorovSmirnovTest#ksSum(...)" returned wrong result in case the provided
+        t-parameters was zero. This affected the calculation of "approximateP(...)" for
+        identical samples.
+      </action>    
       <action dev="tn" type="fix" issue="MATH-1242" due-to="Otmar Ertl"> <!-- backported to 3.6 -->
         Improved performance to calculate the two-sample Kolmogorov-Smirnov test
         via monte carlo simulation ("KolmogorovSmirnovTets#monteCarloP(...)").

src/main/java/org/apache/commons/math4/stat/inference/KolmogorovSmirnovTest.java

@@ -832,7 +832,7 @@ public class KolmogorovSmirnovTest {
      */
     public double ksSum(double t, double tolerance, int maxIterations) {
         if (t == 0.0) {
-            return 1.0;
+            return 0.0;
         }
 
         // TODO: for small t (say less than 1), the alternative expansion in part 3 of [1]

src/test/java/org/apache/commons/math4/stat/inference/KolmogorovSmirnovTestTest.java

@@ -400,11 +400,31 @@ public class KolmogorovSmirnovTestTest {
 
     @Test
     public void testTwoSamplesAllEqual() {
+        int iterations = 10_000;
         final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest();
         for (int i = 2; i < 30; ++i) {
+            // testing values with ties
             double[] values = new double[i];
             Arrays.fill(values, i);
+            // testing values without ties
+            double[] ascendingValues = new double[i];
+            for (int j = 0; j < ascendingValues.length; j++) {
+                ascendingValues[j] = j;
+            }
+
             Assert.assertEquals(0., test.kolmogorovSmirnovStatistic(values, values), 0.);
+            Assert.assertEquals(0., test.kolmogorovSmirnovStatistic(ascendingValues, ascendingValues), 0.);
+
+            if (i < 10) {
+                Assert.assertEquals(1.0, test.exactP(0, values.length, values.length, true), 0.);
+                Assert.assertEquals(1.0, test.exactP(0, values.length, values.length, false), 0.);
+            }
+
+            Assert.assertEquals(1.0, test.monteCarloP(0, values.length, values.length, true, iterations), 0.);
+            Assert.assertEquals(1.0, test.monteCarloP(0, values.length, values.length, false, iterations), 0.);
+
+            Assert.assertEquals(1.0, test.approximateP(0, values.length, values.length), 0.);
+            Assert.assertEquals(1.0, test.approximateP(0, values.length, values.length), 0.);
         }
     }