Use erfinv in the normal distribution.

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1456906 13f79535-47bb-0310-9956-ffa450edef68

src/changes/changes.xml

@@ -55,6 +55,12 @@ This is a minor release: It combines bug fixes and new features.
   Changes to existing features were made in a backwards-compatible
   way such as to allow drop-in replacement of the v3.1[.1] JAR file.
 ">
+      <action dev="luc" type="update"  >
+        Normal distribution now uses a direct implementation of the
+        inverse error function to compute inverse cumulative probability
+        instead of relying on a numerical solver. This is much faster,
+        more accurate and does not need convergence threshold.
+      </action>
       <action dev="luc" type="add" issue="MATH-948" >
         Implementations for inverse error function and inverse complementary
         error functions have been added.

src/main/java/org/apache/commons/math3/distribution/NormalDistribution.java

@@ -19,6 +19,7 @@ package org.apache.commons.math3.distribution;
 
 import org.apache.commons.math3.exception.NotStrictlyPositiveException;
 import org.apache.commons.math3.exception.NumberIsTooLargeException;
+import org.apache.commons.math3.exception.OutOfRangeException;
 import org.apache.commons.math3.exception.util.LocalizedFormats;
 import org.apache.commons.math3.special.Erf;
 import org.apache.commons.math3.util.FastMath;
@@ -152,6 +153,15 @@ public class NormalDistribution extends AbstractRealDistribution {
         return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
     }
 
+    /** {@inheritDoc} */
+    @Override
+    public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
+        if (p < 0.0 || p > 1.0) {
+            throw new OutOfRangeException(p, 0, 1);
+        }
+        return mean + standardDeviation * SQRT2 * Erf.erfInv(2 * p - 1);
+    }
+
     /**
      * {@inheritDoc}
      *