Modified NormalDistributionImpl.cumulativeProbability to return 0 or 1,

respectively for values more than 40 standard deviations from the mean.
For these values, the actual probability is indistinguishable from 0 or 1
as a double.  Top coding improves performance for extreme values and prevents
convergence exceptions.

JIRA: MATH-414

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1040471 13f79535-47bb-0310-9956-ffa450edef68

src/main/java/org/apache/commons/math/distribution/NormalDistributionImpl.java

@@ -114,26 +114,20 @@ public class NormalDistributionImpl extends AbstractContinuousDistribution
 
     /**
      * For this distribution, {@code X}, this method returns {@code P(X < x)}.
+     * If {@code x}is more than 40 standard deviations from the mean, 0 or 1 is returned,
+     * as in these cases the actual value is within {@code Double.MIN_VALUE} of 0 or 1.
      *
      * @param x Value at which the CDF is evaluated.
      * @return CDF evaluated at {@code x}.
-     * @throws MathException if the algorithm fails to converge; unless
+     * @throws MathException if the algorithm fails to converge
-     * {@code x} is more than 20 standard deviations from the mean, in which
-     * case the convergence exception is caught and 0 or 1 is returned.
      */
     public double cumulativeProbability(double x) throws MathException {
-        try {
+        final double dev = x - mean;
-            return 0.5 * (1.0 + Erf.erf((x - mean) /
+        if (FastMath.abs(dev) > 40 * standardDeviation) { 
+            return dev < 0 ? 0.0d : 1.0d;
+        }
+        return 0.5 * (1.0 + Erf.erf((dev) /
                     (standardDeviation * FastMath.sqrt(2.0))));
-        } catch (MaxIterationsExceededException ex) {
-            if (x < (mean - 20 * standardDeviation)) { // JDK 1.5 blows at 38
-                return 0;
-            } else if (x > (mean + 20 * standardDeviation)) {
-                return 1;
-            } else {
-                throw ex;
-            }
-        }
     }
 
     /**

src/site/xdoc/changes.xml

@@ -118,6 +118,13 @@ The <action> type attribute can be add,update,fix,remove.
       </action>
     </release>
     <release version="2.2" date="TBD" description="TBD">
+      <action dev="psteitz" type="fix" issue="MATH-414">
+        Modified NormalDistributionImpl.cumulativeProbability to return 0 or 1,
+        respectively for values more than 40 standard deviations from the mean.
+        For these values, the actual probability is indistinguishable from 0 or 1
+        as a double.  Top coding improves performance for extreme values and prevents
+        convergence exceptions.
+      </action>
       <action dev="psteitz" type="update" issue="MATH-420">
         Added toString() override to StatisticalSummaryValues.
       </action>

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

@@ -152,14 +152,16 @@ public class NormalDistributionTest extends ContinuousDistributionAbstractTest
 
     /**
      * Check to make sure top-coding of extreme values works correctly.
-     * Verifies fix for JIRA MATH-167
+     * Verifies fixes for JIRA MATH-167, MATH-414
      */
     public void testExtremeValues() throws Exception {
         NormalDistribution distribution = new NormalDistributionImpl(0, 1);
-        for (int i = 0; i < 100; i+=5) { // make sure no convergence exception
+        for (int i = 0; i < 100; i++) { // make sure no convergence exception
             double lowerTail = distribution.cumulativeProbability(-i);
             double upperTail = distribution.cumulativeProbability(i);
-            if (i < 10) { // make sure not top-coded
+            if (i < 9) { // make sure not top-coded 
+                // For i = 10, due to bad tail precision in erf (MATH-364), 1 is returned
+                // TODO: once MATH-364 is resolved, replace 9 with 30
                 assertTrue(lowerTail > 0.0d);
                 assertTrue(upperTail < 1.0d);
             }
@@ -168,6 +170,12 @@ public class NormalDistributionTest extends ContinuousDistributionAbstractTest
                 assertTrue(upperTail > 0.99999);
             }
         }
+        
+        assertEquals(distribution.cumulativeProbability(Double.MAX_VALUE), 1, 0);
+        assertEquals(distribution.cumulativeProbability(-Double.MAX_VALUE), 0, 0);
+        assertEquals(distribution.cumulativeProbability(Double.POSITIVE_INFINITY), 1, 0);
+        assertEquals(distribution.cumulativeProbability(Double.NEGATIVE_INFINITY), 0, 0);
+        
    }
 
     public void testMath280() throws MathException {