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Added support for population variance computation. 

git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@141466 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz 2004-10-10 20:40:52 +00:00
parent aa015cae61
commit 55a1e448c2
2 changed files with 109 additions and 11 deletions
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90
src/java/org/apache/commons/math/stat/descriptive/moment/Variance.java
View File

@ -20,7 +20,8 @@ import java.io.Serializable;
import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;
/**
* Computes the (unbiased) sample variance. Uses the definitional formula:
* Computes the variance of the available values. By default, the unbiased
* "sample variance" definitional formula is used:
* <p>
* variance = sum((x_i - mean)^2) / (n - 1)
* <p>
@ -32,13 +33,19 @@ import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStati
* as described in <a href="http://doi.acm.org/10.1145/359146.359152">
* Chan, T. F. andJ. G. Lewis 1979, <i>Communications of the ACM</i>,
* vol. 22 no. 9, pp. 526-531.</a>.
* <p>
* <p>
* The "population variance" ( sum((x_i - mean)^2) / n ) can also
* be computed using this statistic. The <code>isBiasCorrected</code>
* property determines whether the "population" or "sample" value is
* returned by the <code>evaluate</code> and <code>getResult</code> methods.
* To compute population variances, set this property to <code>false.</code>
*
* <strong>Note that this implementation is not synchronized.</strong> If
* multiple threads access an instance of this class concurrently, and at least
* one of the threads invokes the <code>increment()</code> or
* <code>clear()</code> method, it must be synchronized externally.
*
* @version $Revision: 1.1 $ $Date: 2004/10/08 05:08:17 $
* @version $Revision: 1.2 $ $Date: 2004/10/10 20:40:52 $
*/
public class Variance extends AbstractStorelessUnivariateStatistic implements Serializable {
@ -54,6 +61,13 @@ public class Variance extends AbstractStorelessUnivariateStatistic implements Se
* constructed with an external SecondMoment as a parameter.
*/
protected boolean incMoment = true;
/**
* Determines whether or not bias correction is applied when computing the
* value of the statisic. True means that bias is corrected. See
* {@link Variance} for details on the formula.
*/
private boolean isBiasCorrected = true;
/**
* Constructs a Variance.
@ -64,6 +78,7 @@ public class Variance extends AbstractStorelessUnivariateStatistic implements Se
/**
* Constructs a Variance based on an external second moment.
*
* @param m2 the SecondMoment (Thrid or Fourth moments work
* here as well.)
*/
@ -71,6 +86,36 @@ public class Variance extends AbstractStorelessUnivariateStatistic implements Se
incMoment = false;
this.moment = m2;
}
/**
* Constructs a Variance with the specified <code>isBiasCorrected</code>
* property
*
* @param isBiasCorrected setting for bias correction - true means
* bias will be corrected and is equivalent to using the argumentless
* constructor
*/
public Variance(boolean isBiasCorrected) {
moment = new SecondMoment();
this.isBiasCorrected = isBiasCorrected;
}
/**
* Constructs a Variance with the specified <code>isBiasCorrected</code>
* property and the supplied external second moment.
*
* @param isBiasCorrected setting for bias correction - true means
* bias will be corrected and is equivalent to using the argumentless
* constructor
* @param m2 the SecondMoment (Thrid or Fourth moments work
* here as well.)
*/
public Variance(boolean isBiasCorrected, SecondMoment m2) {
incMoment = false;
this.moment = m2;
this.isBiasCorrected = isBiasCorrected;
}
/**
* @see org.apache.commons.math.stat.descriptive.StorelessUnivariateStatistic#increment(double)
*/
@ -89,7 +134,11 @@ public class Variance extends AbstractStorelessUnivariateStatistic implements Se
} else if (moment.n == 1) {
return 0d;
} else {
return moment.m2 / ((double) moment.n - 1d);
if (isBiasCorrected) {
return moment.m2 / ((double) moment.n - 1d);
} else {
return moment.m2 / ((double) moment.n);
}
}
}
@ -210,8 +259,13 @@ public class Variance extends AbstractStorelessUnivariateStatistic implements Se
accum += Math.pow((values[i] - mean), 2.0);
accum2 += (values[i] - mean);
}
var = (accum - (Math.pow(accum2, 2) / ((double) length))) /
(double) (length - 1);
if (isBiasCorrected) {
var = (accum - (Math.pow(accum2, 2) / ((double) length))) /
(double) (length - 1);
} else {
var = (accum - (Math.pow(accum2, 2) / ((double) length))) /
(double) length;
}
}
}
return var;
@ -224,10 +278,12 @@ public class Variance extends AbstractStorelessUnivariateStatistic implements Se
* <p>
* See {@link Variance} for details on the computing algorithm.
* <p>
* The formula used assumes that the supplied mean value is the arithmetic
* mean of the sample data, not a known population parameter. This method
* is supplied only to save computation when the mean has already been
* computed.
* If <code>isBiasCorrected</code> is <code>true</code> the formula used
* assumes that the supplied mean value is the arithmetic mean of the
* sample data, not a known population parameter. If the mean is a known
* population parameter, or if the "population" version of the variance is
* desired, set <code>isBiasCorrected</code> to <code>false</code> before
* invoking this method.
* <p>
* Returns 0 for a single-value (i.e. length = 1) sample.
* <p>
@ -244,4 +300,18 @@ public class Variance extends AbstractStorelessUnivariateStatistic implements Se
return evaluate(values, mean, 0, values.length);
}
/**
* @return Returns the isBiasCorrected.
*/
public boolean isBiasCorrected() {
return isBiasCorrected;
}
/**
* @param isBiasCorrected The isBiasCorrected to set.
*/
public void setBiasCorrected(boolean isBiasCorrected) {
this.isBiasCorrected = isBiasCorrected;
}
}

30
src/test/org/apache/commons/math/stat/descriptive/moment/VarianceTest.java
View File

@ -24,7 +24,7 @@ import org.apache.commons.math.stat.descriptive.UnivariateStatistic;
/**
* Test cases for the {@link UnivariateStatistic} class.
*
* @version $Revision: 1.1 $ $Date: 2004/10/08 05:08:20 $
* @version $Revision: 1.2 $ $Date: 2004/10/10 20:40:52 $
*/
public class VarianceTest extends StorelessUnivariateStatisticAbstractTest{
@ -67,5 +67,33 @@ public class VarianceTest extends StorelessUnivariateStatisticAbstractTest{
std.increment(1d);
assertEquals(0d, std.getResult(), 0);
}
/**
* Test population version of variance
*/
public void testPopulation() {
double[] values = {-1.0d, 3.1d, 4.0d, -2.1d, 22d, 11.7d, 3d, 14d};
SecondMoment m = new SecondMoment();
m.evaluate(values); // side effect is to add values
Variance v1 = new Variance();
v1.setBiasCorrected(false);
assertEquals(populationVariance(values), v1.evaluate(values), 1E-14);
v1.incrementAll(values);
assertEquals(populationVariance(values), v1.getResult(), 1E-14);
v1 = new Variance(false, m);
assertEquals(populationVariance(values), v1.getResult(), 1E-14);
}
/**
* Definitional formula for population variance
*/
protected double populationVariance(double[] v) {
double mean = new Mean().evaluate(v);
double sum = 0;
for (int i = 0; i < v.length; i++) {
sum += (v[i] - mean) * (v[i] - mean);
}
return sum / (double) v.length;
}
}