diff --git a/pom.xml b/pom.xml
index e43cd5f..920b26b 100644
--- a/pom.xml
+++ b/pom.xml
@@ -1,4 +1,5 @@
-<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+<project xmlns="http://maven.apache.org/POM/4.0.0"
+  xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
   xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/maven-v4_0_0.xsd">
   <modelVersion>4.0.0</modelVersion>
   <groupId>info.istlab.Zemi01</groupId>
@@ -24,8 +25,15 @@
       <version>3.8.1</version>
       <scope>test</scope>
     </dependency>
-  </dependencies>
 
+    <!-- https://mvnrepository.com/artifact/org.apache.commons/commons-math3 -->
+    <dependency>
+      <groupId>org.apache.commons</groupId>
+      <artifactId>commons-math3</artifactId>
+      <version>3.6.1</version>
+    </dependency>
+
+  </dependencies>
 
   <build>
     <plugins>
@@ -44,8 +52,8 @@
           <!-- 成果物の名前にassemblyがidを振ってしまうのを無効にする -->
           <!-- <appendAssemblyId>false</appendAssemblyId> -->
           <!-- <descriptors>
-             include/excludeなどの設定は外部ファイルに記述する 
-            <descriptor>assembly.xml</descriptor>
+             include/excludeなどの設定は外部ファイルに記述する
+          <descriptor>assembly.xml</descriptor>
           </descriptors> -->
           <descriptorRefs>
             <descriptorRef>jar-with-dependencies</descriptorRef>
@@ -67,4 +75,4 @@
     </plugins>
 
   </build>
-</project>
+</project>
\ No newline at end of file
diff --git a/src/main/java/info/istlab/Zemi01/Ttest.java b/src/main/java/info/istlab/Zemi01/Ttest.java
index ac2fca1..f54c4a8 100644
--- a/src/main/java/info/istlab/Zemi01/Ttest.java
+++ b/src/main/java/info/istlab/Zemi01/Ttest.java
@@ -1,22 +1,23 @@
 package info.istlab.Zemi01;
 
+import org.apache.commons.math3.distribution.TDistribution;
+
 public class Ttest {
     public static void main(String[] args) {
         double[] d1 = { 321, 269, 341, 318, 297, 308, 343, 337, 329 };
         double[] d2 = { 303, 253, 283, 333, 307, 310, 296, 265, 271 };
         double t1, t2;
         System.out.println(t1 = paired_t(d1, d2));
-        double p1 = tdist(t1, d1.length-1, 2);
-        System.out.println(p1);
-
+        double p1 = tdist(t1, d1.length - 1, 2);
+        System.out.println("p1 = "+p1);
 
         System.out.println("----");
 
-        System.out.println(t2 = welch_t(d1, d2));
+        System.out.println("t2 = "+ (t2 = welch_t(d1, d2)));
         double df2 = welch_degree_of_freedom(d1, d2);
-        System.out.println("df2 = "+df2);
-        double p2 = tdist(t2,df2, 1);
-        System.out.println(p2);
+        System.out.println("df2 = " + df2);
+        double p2 = tdist(t2, df2, 2);
+        System.out.println("p2 = "+p2);
     }
 
     /**
@@ -101,25 +102,45 @@
         double diff_avg = avg(ary1) - avg(ary2);
         return diff_avg / Math.sqrt(stddev1 + stddev2);
     }
-    public static double welch_degree_of_freedom(double[] ary1, double[] ary2){
+
+    public static double welch_degree_of_freedom(double[] ary1, double[] ary2) {
         // 不偏分散/データ数
         double stddev1 = var(ary1) / ary1.length;
         double stddev2 = var(ary2) / ary2.length;
         double a1 = Math.pow(stddev1 + stddev2, 2);
-        double b1 = Math.pow(stddev1,2)/(ary1.length-1) + Math.pow(stddev2,2)/(ary2.length-1);
-        return a1/b1;        
+        double b1 = Math.pow(stddev1, 2) / (ary1.length - 1) + Math.pow(stddev2, 2) / (ary2.length - 1);
+        return a1 / b1;
     }
 
     /**
-     * TDIST
+     * TDIST by commons-math3 TDistribution
+     * 
      * @param x
      * @param df
      * @param tails
      * @return
      */
-    public static double tdist(double x, double deg_free, int tails){
-        return (1.0d - studentsCdf(x, deg_free)) * tails;
+    public static double tdist(double x, double deg_free, int tails) {
+        TDistribution tdistobj = new TDistribution(deg_free);
+        double cdf = tdistobj.cumulativeProbability(x);
+        double ret = (1-cdf) * tails;
+        // //test
+        // double test = tdist_old(x, deg_free, tails);
+        // if (test != ret) System.out.println("DIFF ret = "+ret+"  test "+test );
+        return ret;
     }
+
+    /**
+     * 
+     * @param x
+     * @param deg_free
+     * @param tails
+     * @return
+     */
+    public static double tdist_old(double x, double deg_free, int tails) {
+        return (1-studentsCdf(x, deg_free)) * tails;
+    }
+
     /**
      * 
      * http://www.java2s.com/example/java-api/java/lang/math/exp-1-32.html
@@ -163,7 +184,7 @@
      * Log Gamma Function
      * 
      * @param Z
-     * @return 
+     * @return
      */
     public static double logGamma(double Z) {
         double S = 1.0 + 76.18009173 / Z - 86.50532033 / (Z + 1.0) + 24.01409822 / (Z + 2.0)
@@ -172,13 +193,14 @@
 
         return LG;
     }
+
     /**
      * Internal function used by StudentCdf
      * 
      * @param x
      * @param A
      * @param B
-     * @return 
+     * @return
      */
     protected static double betinc(double x, double A, double B) {
         double A0 = 0.0;
@@ -187,7 +209,7 @@
         double B1 = 1.0;
         double M9 = 0.0;
         double A2 = 0.0;
-        while (Math.abs((A1 - A2) / A1) > 0.00000000000000001) {
+        while (Math.abs((A1 - A2) / A1) > 0.00000001) {
             A2 = A1;
             double C9 = -(A + M9) * (A + B + M9) * x / (A + 2.0 * M9) / (A + 2.0 * M9 + 1.0);
             A0 = A1 + C9 * A0;
@@ -204,4 +226,78 @@
         return A1 / A;
     }
 
+    /**
+     * うまくいかないので使わない
+     * @param x
+     * @param v
+     * @return
+     */
+    public static double studentsCdf2(double x, double v) {
+        double xL = x;
+        double xR = 100000;
+        int n = 10000;
+        double goukei = 0.0;
+        double a, b, xc, tmp;
+        double dx = (xR - xL) / n;
+        double B = simpson_betafunc(0.5, v / 2);
+        // double B = Beta.regularizedBeta(0.5, v / 2);
+        for (int i = 0; i < n; i++) {
+            a = xL + i * dx;
+            b = a + dx;
+            xc = a + dx / 2.0;
+            tmp = 0.0;
+            tmp = tmp + densityfunc(a, v, B) / 3;
+            tmp = tmp + densityfunc(xc, v, B) * 4 / 3;
+            tmp = tmp + densityfunc(b, v, B) / 3;
+            tmp = tmp * dx / 2;
+            goukei += tmp;
+        }
+        return goukei;
+    }
+
+    private static double densityfunc(double x, double v, double B) {
+        return Math.pow(1.0 + (x * x / v), -(v + 1) / 2) / (Math.sqrt(v) * B);
+    }
+
+    /**
+     * うまくいかないので使わない
+     * @param u
+     * @param v
+     * @return
+     */
+    public static double simpson_betafunc(double u, double v) {
+        double xL = 0.0;
+        double xR = 1.0;
+        int n = 100;
+        double goukei = 0.0;
+        double a, b, xc, tmp;
+        double dx = (xR - xL) / n;
+        for (int i = 0; i < n; i++) {
+            a = xL + i * dx;
+            b = a + dx;
+            xc = a + dx / 2.0;
+            tmp = 0.0;
+            tmp = tmp + bfunc(a, u, v) / 3;
+            tmp = tmp + bfunc(xc, u, v) * 4 / 3;
+            tmp = tmp + bfunc(b, u, v) / 3;
+            tmp = tmp * dx / 2;
+            goukei += tmp;
+            System.out.println(i+" "+tmp+" "+goukei);
+        }
+        return goukei;
+    }
+
+    /**
+     * うまくいかないので使わない
+     * @param x
+     * @param u
+     * @param v
+     * @return
+     */
+    private static double bfunc(double x, double u, double v) {
+        double d =  Math.pow(x, u - 1) * Math.pow(1.0 - x, v - 1);
+        System.out.println("bfunc "+x+" "+u+" "+v+" = "+d);
+        return d;
+    }
+
 }