Patch adds getSkewness and getKurtosis to Univariate and an implimentation

in UnivariateImpl. It also adds test for NaN and 0.0 to UnivariateImplTest

PR: Issue 20250
Obtained from: Bugzilla
Submitted by: Mark Diggory
Reviewed by: Tim O'Brien


git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@140866 13f79535-47bb-0310-9956-ffa450edef68

src/java/org/apache/commons/math/Univariate.java

@@ -73,7 +73,7 @@
  * @author Phil Steitz
  * @author <a href="mailto:tobrien@apache.org">Tim O'Brien</a>
  * @author Mark Diggory
- * @version $Revision: 1.7 $ $Date: 2003/05/26 17:40:20 $
+ * @version $Revision: 1.8 $ $Date: 2003/05/29 19:49:18 $
  * 
 */
 public interface Univariate {
@@ -132,6 +132,26 @@ public interface Univariate {
      */
     abstract double getStandardDeviation();
 
+	/**
+     * Returns the skewness of a given distribution.  Skewness is a 
+     * measure of the assymetry of a given distribution. <p>
+	 * Double.NaN is returned for an empty set of values and 0.0 is 
+	 * returned for a value set &lt;=2. 
+	 * 
+	 * @return Value of property skewness.
+	 */
+	abstract double getSkewness();
+	
+	/**
+     * Returns the Kurtosis of the available values. Kurtosis is a 
+     * measure of the "peakedness" of a distribution <p>
+     * Double.NaN is returned for an empty set of values and 0.0 is 
+     * returned for a value set &lt;=3. 
+     * 
+     * @return Value of property kurtosis.
+	 */
+	abstract double getKurtosis();
+		
     /** 
      * Returns the maximum of the available values <p>
      * Double.NaN is returned in no values have been added

src/java/org/apache/commons/math/UnivariateImpl.java

@@ -67,7 +67,7 @@ import java.io.Serializable;
  * @author <a href="mailto:tobrien@apache.org">Tim O'Brien</a>
  * @author Mark Diggory
  * @author Brent Worden
- * @version $Revision: 1.8 $ $Date: 2003/05/26 17:40:20 $
+ * @version $Revision: 1.9 $ $Date: 2003/05/29 19:49:18 $
  * 
 */
 public class UnivariateImpl implements Univariate, Serializable {
@@ -86,6 +86,12 @@ public class UnivariateImpl implements Univariate, Serializable {
     /** running sum of squares that have been added */
     private double sumsq = 0.0;
 
+	/** running sum of 3rd powers that have been added */
+	private double sumCube = 0.0;
+	
+	/** running sum of 4th powers that have been added */
+	private double sumQuad = 0.0;
+	
     /** count of values that have been added */
     private int n = 0;
 
@@ -162,6 +168,44 @@ public class UnivariateImpl implements Univariate, Serializable {
         }
     }
    
+   
+	/**
+	 * Returns the skewness of the values that have been added as described by
+     * <a href=http://mathworld.wolfram.com/k-Statistic.html>Equation (6) for k-Statistics</a>.
+     * 
+	 * @return The skew of a set of values.  Double.NaN is returned for
+	 *         an empty set of values and 0.0 is returned for a &lt;= 2 value set.
+	 */
+	public double getSkewness() {
+		
+		if( n < 1) return Double.NaN;
+		if( n <= 2 ) return 0.0;                  
+			
+		return ( 2*Math.pow(sum,3) - 3*sum*sumsq + ((double)n)*((double)n)*sumCube ) / 
+			   ( ((double)n)*(((double)n)-1)*(((double)n)-2));  
+	}
+	
+	/**
+	 * Returns the kurtosis of the values that have been added as described by
+     * <a href=http://mathworld.wolfram.com/k-Statistic.html>Equation (7) for k-Statistics</a>.
+     * 
+	 * @return The kurtosis of a set of values.  Double.NaN is returned for
+	 *         an empty set of values and 0.0 is returned for a &lt;= 3 value set.
+	 */
+	public double getKurtosis() {
+		
+		if( n < 1) return Double.NaN;
+		if( n <= 3 ) return 0.0;
+		
+		double x1 = -6*Math.pow(sum,4);
+		double x2 = 12*((double)n)*Math.pow(sum,2)*sumsq;
+		double x3 = -3*((double)n)*(((double)n)-1)*Math.pow(sumsq,2);
+		double x4 = -4*((double)n)*(((double)n)+1)*sum*sumCube;
+		double x5 = Math.pow(((double)n),2)*(((double)n)+1)*sumQuad;
+		return (x1 + x2 + x3 + x4 + x5) / 
+		       (((double)n)*(((double)n)-1)*(((double)n)-2)*(((double)n)-3));
+	} 
+	
     private void insertValue(double v) {
 
         // The default value of product is NaN, if you
@@ -176,14 +220,15 @@ public class UnivariateImpl implements Univariate, Serializable {
         }
 
         if( windowSize != Univariate.INFINITE_WINDOW ) {
-
             if( windowSize == n ) {
                 double discarded = doubleArray.addElementRolling( v );
 
                 // Remove the influence of the discarded
                 sum -= discarded;
                 sumsq -= discarded * discarded;
-
+				sumCube -= Math.pow(discarded,3);
+				sumQuad -= Math.pow(discarded,4); 
+				
                 if(discarded == min) {
                     min = doubleArray.getMin();
                 } else {
@@ -192,9 +237,6 @@ public class UnivariateImpl implements Univariate, Serializable {
                     }
                 } 
                 
-                sum += v;
-                sumsq += v*v;
-
                 if(product != 0.0){
                     // can safely remove discarded value
                     product *= v/discarded;
@@ -203,7 +245,7 @@ public class UnivariateImpl implements Univariate, Serializable {
                     product = 1.0;
                     double[] elements = doubleArray.getElements();
                     for( int i = 0; i < elements.length; i++ ) {
-                    product *= elements[i];
+                    	product *= elements[i];
                     }
                 } // else product = 0 and will still be 0 after discard
 
@@ -212,8 +254,6 @@ public class UnivariateImpl implements Univariate, Serializable {
                 n += 1.0;
                 if (v < min) min = v;
                 if (v > max) max = v;
-                sum += v;
-                sumsq += v*v;
                 product *= v;
             }
         } else {
@@ -223,10 +263,13 @@ public class UnivariateImpl implements Univariate, Serializable {
             n += 1.0;
             if (v < min) min = v;
             if (v > max) max = v;
-            sum += v;
-            sumsq += v*v;
             product *= v;
         }
+        
+		sum += v;
+		sumsq += v*v;
+		sumCube += Math.pow(v,3);
+		sumQuad += Math.pow(v,4);
     }
 
     /** Getter for property max.
@@ -272,6 +315,20 @@ public class UnivariateImpl implements Univariate, Serializable {
         return sumsq;
     }
 
+	/** Getter for property sumCube.
+	 * @return Value of property sumCube.
+	 */
+	public double getSumCube() {
+		return sumCube;
+	}
+	
+	/** Getter for property sumQuad.
+	 * @return Value of property sumQuad.
+	 */
+	public double getSumQuad() {
+		return sumQuad;
+	}
+	
     /**
      * Generates a text report displaying 
      * univariate statistics from values that
@@ -286,13 +343,14 @@ public class UnivariateImpl implements Univariate, Serializable {
         outBuffer.append("max: " + max + "\n");
         outBuffer.append("mean: " + getMean() + "\n");
         outBuffer.append("std dev: " + getStandardDeviation() + "\n");
+		outBuffer.append("skewness: " + getSkewness() + "\n");
+		outBuffer.append("kurtosis: " + getKurtosis() + "\n");
         return outBuffer.toString();
     }
     
     /** Resets all sums to 0, resets min and max */
     public void clear() {
-        this.sum = 0.0;
+        this.sum = this.sumsq = this.sumCube = this.sumQuad = 0.0;
-        this.sumsq = 0.0;
         this.n = 0;
         this.min = Double.MAX_VALUE;
         this.max = Double.MIN_VALUE;

src/test/org/apache/commons/math/UnivariateImplTest.java

@@ -62,7 +62,7 @@ import junit.framework.TestSuite;
  *
  * @author Phil Steitz
  * @author Tim Obrien
- * @version $Revision: 1.3 $ $Date: 2003/05/23 17:33:18 $
+ * @version $Revision: 1.4 $ $Date: 2003/05/29 19:49:18 $
  */
 
 public final class UnivariateImplTest extends TestCase {
@@ -117,19 +117,54 @@ public final class UnivariateImplTest extends TestCase {
     	UnivariateImpl u = new UnivariateImpl();
         assertTrue("Mean of n = 0 set should be NaN", 
             Double.isNaN( u.getMean() ) );
-	assertTrue("Standard Deviation of n = 0 set should be NaN", 
+		assertTrue("Standard Deviation of n = 0 set should be NaN", 
             Double.isNaN( u.getStandardDeviation() ) );
-	assertTrue("Variance of n = 0 set should be NaN", 
+		assertTrue("Variance of n = 0 set should be NaN", 
             Double.isNaN(u.getVariance() ) );
+		assertTrue("skew of n = 0 set should be NaN",
+			Double.isNaN(u.getSkewness() ) );	
+		assertTrue("kurtosis of n = 0 set should be NaN", 
+			Double.isNaN(u.getKurtosis() ) );		
+		
 	
-        u.addValue(one);
+		/* n=1 */
+		u.addValue(one);
+		assertTrue("mean should be one (n = 1)", 
+			u.getMean() == one);
+		assertTrue("geometric should be one (n = 1)", 
+			u.getGeometricMean() == one);
+		assertTrue("Std should be zero (n = 1)", 
+			u.getStandardDeviation() == 0.0);
+		assertTrue("variance should be zero (n = 1)", 
+			u.getVariance() == 0.0);
+		assertTrue("skew should be zero (n = 1)", 
+			u.getSkewness() == 0.0);
+		assertTrue("kurtosis should be zero (n = 1)", 
+			u.getKurtosis() == 0.0);		
+					
+		/* n=2 */				
+		u.addValue(twoF);
+		assertTrue("Std should not be zero (n = 2)", 
+			u.getStandardDeviation() != 0.0);
+		assertTrue("variance should not be zero (n = 2)", 
+			u.getVariance() != 0.0);
+		assertTrue("skew should not be zero (n = 2)", 
+			u.getSkewness() == 0.0);
+		assertTrue("kurtosis should be zero (n = 2)", 
+			u.getKurtosis() == 0.0);
 
-	assertTrue( "Mean of n = 1 set should be value of single item n1", 
+		/* n=3 */
-            u.getMean() == one);
+		u.addValue(twoL);
-	assertTrue( "Mean of n = 1 set should be zero", 
+		assertTrue("skew should not be zero (n = 3)", 
-            u.getStandardDeviation() == 0);
+			u.getSkewness() != 0.0);
-	assertTrue( "Variance of n = 1 set should be zero",
+		assertTrue("kurtosis should be zero (n = 3)", 
-            u.getVariance() == 0);	
+			u.getKurtosis() == 0.0);
+        
+		/* n=4 */
+		u.addValue(three);
+		assertTrue("kurtosis should not be zero (n = 4)", 
+			u.getKurtosis() != 0.0);        
+            
     }
 
     public void testProductAndGeometricMean() throws Exception {
@@ -199,9 +234,5 @@ public final class UnivariateImplTest extends TestCase {
         
         //FiXME: test all other NaN contract specs
     }
-        
-        
-        
-
-}
 
+}