MATH-1257

Increased accuracy.

src/changes/changes.xml

@@ -54,6 +54,10 @@ If the output is not quite correct, check for invisible trailing spaces!
     </release>
 
     <release version="4.0" date="XXXX-XX-XX" description="">
+      <action dev="erans" type="fix" issue="MATH-1257" due-to="Bill Murphy">
+        Better accuracy in computation of cumulative probability of "NormalDistribution"
+        (package "o.a.c.m.distribution").
+      </action>
       <action dev="erans" type="fix" issue="MATH-1256"> <!-- backported to 3.6 -->
         Boundary check to construct an "Interval" (package "o.a.c.m.geometry.euclidean.oned").
       </action>

src/main/java/org/apache/commons/math4/distribution/NormalDistribution.java

@@ -193,7 +193,7 @@ public class NormalDistribution extends AbstractRealDistribution {
         if (FastMath.abs(dev) > 40 * standardDeviation) {
             return dev < 0 ? 0.0d : 1.0d;
         }
-        return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
+        return 0.5 * Erf.erfc(-dev / (standardDeviation * SQRT2));
     }
 
     /** {@inheritDoc}

src/test/java/org/apache/commons/math4/distribution/NormalDistributionTest.java

@@ -111,6 +111,17 @@ public class NormalDistributionTest extends RealDistributionAbstractTest {
         verifyInverseCumulativeProbabilities();
     }
 
+    // MATH-1257
+    @Test
+    public void testCumulativeProbability() {
+        final RealDistribution dist = new NormalDistribution(0, 1);
+        double x = -10;
+        double expected = 7.61985e-24;
+        double v = dist.cumulativeProbability(x);
+        double tol = 1e-5;
+        Assert.assertEquals(1, v / expected, 1e-5);
+    }
+
     @Test
     public void testGetMean() {
         NormalDistribution distribution = (NormalDistribution) getDistribution();