From 9df5e9419d83c11b4a2c3421c5ff7ea1f544366b Mon Sep 17 00:00:00 2001
From: Kexin Xie <kexin.xie@salesforce.com>
Date: Sun, 7 May 2017 09:47:14 -0700
Subject: [PATCH] fix a bug that sometimes Binomial test return probability
 greater than 1

---
 .../math4/stat/inference/BinomialTest.java    |  6 ++-
 .../stat/inference/BinomialTestTest.java      | 48 +++++++++++++++++++
 2 files changed, 53 insertions(+), 1 deletion(-)

diff --git a/src/main/java/org/apache/commons/math4/stat/inference/BinomialTest.java b/src/main/java/org/apache/commons/math4/stat/inference/BinomialTest.java
index 2846c6819..4a941305a 100644
--- a/src/main/java/org/apache/commons/math4/stat/inference/BinomialTest.java
+++ b/src/main/java/org/apache/commons/math4/stat/inference/BinomialTest.java
@@ -135,7 +135,11 @@ public class BinomialTest {
                 double pHigh = distribution.probability(criticalValueHigh);
 
                 if (pLow == pHigh) {
-                    pTotal += 2 * pLow;
+                    if (criticalValueLow == criticalValueHigh) {
+                        pTotal += pLow;
+                    } else {
+                        pTotal += 2 * pLow;
+                    }
                     criticalValueLow++;
                     criticalValueHigh--;
                 } else if (pLow < pHigh) {
diff --git a/src/test/java/org/apache/commons/math4/stat/inference/BinomialTestTest.java b/src/test/java/org/apache/commons/math4/stat/inference/BinomialTestTest.java
index 365f21dc8..55e1730ad 100644
--- a/src/test/java/org/apache/commons/math4/stat/inference/BinomialTestTest.java
+++ b/src/test/java/org/apache/commons/math4/stat/inference/BinomialTestTest.java
@@ -42,6 +42,54 @@ public class BinomialTestTest {
             trials, successes, probability, AlternativeHypothesis.GREATER_THAN), 1E-4);
         Assert.assertEquals(0.982, testStatistic.binomialTest(
             trials, successes, probability, AlternativeHypothesis.LESS_THAN), 1E-4);
+
+        // for special boundary conditions
+        Assert.assertEquals(1, testStatistic.binomialTest(
+            3, 3, 1, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(1, testStatistic.binomialTest(
+            3, 3, 0.9, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(1, testStatistic.binomialTest(
+            3, 3, 0.8, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.559, testStatistic.binomialTest(
+            3, 3, 0.7, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.28, testStatistic.binomialTest(
+            3, 3, 0.6, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.25, testStatistic.binomialTest(
+            3, 3, 0.5, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.064, testStatistic.binomialTest(
+            3, 3, 0.4, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.027, testStatistic.binomialTest(
+            3, 3, 0.3, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.008, testStatistic.binomialTest(
+            3, 3, 0.2, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.001, testStatistic.binomialTest(
+            3, 3, 0.1, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0, testStatistic.binomialTest(
+            3, 3, 0.0, AlternativeHypothesis.TWO_SIDED), 1E-4);
+
+        Assert.assertEquals(0, testStatistic.binomialTest(
+            3, 0, 1, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.001, testStatistic.binomialTest(
+            3, 0, 0.9, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.008, testStatistic.binomialTest(
+            3, 0, 0.8, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.027, testStatistic.binomialTest(
+            3, 0, 0.7, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.064, testStatistic.binomialTest(
+            3, 0, 0.6, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.25, testStatistic.binomialTest(
+            3, 0, 0.5, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.28, testStatistic.binomialTest(
+            3, 0, 0.4, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(0.559, testStatistic.binomialTest(
+            3, 0, 0.3, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(1, testStatistic.binomialTest(
+            3, 0, 0.2, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(1, testStatistic.binomialTest(
+            3, 0, 0.1, AlternativeHypothesis.TWO_SIDED), 1E-4);
+        Assert.assertEquals(1, testStatistic.binomialTest(
+            3, 0, 0.0, AlternativeHypothesis.TWO_SIDED), 1E-4);
+
     }
 
     @Test