http://commons.apache.org/proper/commons-math/: The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang. (The Apache Software Foundation)
  • Eldar Agalarov
  • Tim Allison
  • C. Scott Ananian
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  • Jared Becksfort
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  • Elliotte Rusty Harold
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  • Kim van der Linde
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/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.stat.descriptive.moment;

import java.io.Serializable;

import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.stat.descriptive.WeightedEvaluation;
import org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic;
import org.apache.commons.math3.util.MathUtils;


Computes the variance of the available values.  By default, the unbiased
"sample variance" definitional formula is used:


variance = sum((x_i - mean)^2) / (n - 1) 


 where mean is the Mean and n is the number
of sample observations.



The definitional formula does not have good numerical properties, so
this implementation does not compute the statistic using the definitional
formula. 
    

  •  The getResult method computes the variance using
updating formulas based on West's algorithm, as described in
 Chan, T. F. and
J. G. Lewis 1979, Communications of the ACM,
vol. 22 no. 9, pp. 526-531.
    • 

  •  The evaluate methods leverage the fact that they have the
full array of values in memory to execute a two-pass algorithm.
Specifically, these methods use the "corrected two-pass algorithm" from
Chan, Golub, Levesque, Algorithms for Computing the Sample Variance,
American Statistician, vol. 37, no. 3 (1983) pp. 242-247.

Note that adding values using increment or
incrementAll and then executing getResult will
sometimes give a different, less accurate, result than executing
evaluate with the full array of values. The former approach
should only be used when the full array of values is not available.



The "population variance"  ( sum((x_i - mean)^2) / n ) can also
be computed using this statistic.  The isBiasCorrected
property determines whether the "population" or "sample" value is
returned by the evaluate and getResult methods.
To compute population variances, set this property to false.




Note that this implementation is not synchronized. If
multiple threads access an instance of this class concurrently, and at least
one of the threads invokes the increment() or
clear() method, it must be synchronized externally.


/**
 * 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>
 * <p>
 * where mean is the {@link Mean} and <code>n</code> is the number
 * of sample observations.</p>
 * <p>
 * The definitional formula does not have good numerical properties, so
 * this implementation does not compute the statistic using the definitional
 * formula. <ul>
 * <li> The <code>getResult</code> method computes the variance using
 * updating formulas based on West's algorithm, as described in
 * <a href="http://doi.acm.org/10.1145/359146.359152"> Chan, T. F. and
 * J. G. Lewis 1979, <i>Communications of the ACM</i>,
 * vol. 22 no. 9, pp. 526-531.</a></li>
 * <li> The <code>evaluate</code> methods leverage the fact that they have the
 * full array of values in memory to execute a two-pass algorithm.
 * Specifically, these methods use the "corrected two-pass algorithm" from
 * Chan, Golub, Levesque, <i>Algorithms for Computing the Sample Variance</i>,
 * American Statistician, vol. 37, no. 3 (1983) pp. 242-247.</li></ul>
 * Note that adding values using <code>increment</code> or
 * <code>incrementAll</code> and then executing <code>getResult</code> will
 * sometimes give a different, less accurate, result than executing
 * <code>evaluate</code> with the full array of values. The former approach
 * should only be used when the full array of values is not available.</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>
 * </p>
 * <p>
 * <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.</p>
 *
 */
public class Variance extends AbstractStorelessUnivariateStatistic implements Serializable, WeightedEvaluation {

    
Serializable version identifier 
/** Serializable version identifier */
    private static final long serialVersionUID = -9111962718267217978L;

    
SecondMoment is used in incremental calculation of Variance
/** SecondMoment is used in incremental calculation of Variance*/
    protected SecondMoment moment = null;

    
Whether or not increment(double) should increment the internal second moment. When a Variance is constructed with an external SecondMoment as a constructor parameter, this property is set to false and increments must be applied to the second moment directly. 
/**
     * Whether or not {@link #increment(double)} should increment
     * the internal second moment. When a Variance is constructed with an
     * external SecondMoment as a constructor parameter, this property is
     * set to false and increments must be applied to the second moment
     * directly.
     */
    protected boolean incMoment = true;

    
Whether or not bias correction is applied when computing the value of the statistic. True means that bias is corrected. See Variance for details on the formula. 
/**
     * Whether or not bias correction is applied when computing the
     * value of the statistic. True means that bias is corrected.  See
     * {@link Variance} for details on the formula.
     */
    private boolean isBiasCorrected = true;

    
Constructs a Variance with default (true) isBiasCorrected
property.

/**
     * Constructs a Variance with default (true) <code>isBiasCorrected</code>
     * property.
     */
    public Variance() {
        moment = new SecondMoment();
    }

    
Constructs a Variance based on an external second moment. When this constructor is used, the statistic may only be incremented via the moment, i.e., increment(double) does nothing; whereas m2.increment(value) increments both m2 and the Variance instance constructed from it. 
Params:
  • m2 – the SecondMoment (Third or Fourth moments work
here as well.)
/**
     * Constructs a Variance based on an external second moment.
     * When this constructor is used, the statistic may only be
     * incremented via the moment, i.e., {@link #increment(double)}
     * does nothing; whereas {@code m2.increment(value)} increments
     * both {@code m2} and the Variance instance constructed from it.
     *
     * @param m2 the SecondMoment (Third or Fourth moments work
     * here as well.)
     */
    public Variance(final SecondMoment m2) {
        incMoment = false;
        this.moment = m2;
    }

    
Constructs a Variance with the specified isBiasCorrected
property

Params:
  • isBiasCorrected –  setting for bias correction - true means
bias will be corrected and is equivalent to using the argumentless
constructor
/**
     * 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 isBiasCorrected
property and the supplied external second moment.

Params:
  • isBiasCorrected –  setting for bias correction - true means
bias will be corrected
  • m2 – the SecondMoment (Third or Fourth moments work
here as well.)
/**
     * 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
     * @param m2 the SecondMoment (Third or Fourth moments work
     * here as well.)
     */
    public Variance(boolean isBiasCorrected, SecondMoment m2) {
        incMoment = false;
        this.moment = m2;
        this.isBiasCorrected = isBiasCorrected;
    }

    
Copy constructor, creates a new Variance identical to the original 
Params:
  • original – the Variance instance to copy
Throws:
/**
     * Copy constructor, creates a new {@code Variance} identical
     * to the {@code original}
     *
     * @param original the {@code Variance} instance to copy
     * @throws NullArgumentException if original is null
     */
    public Variance(Variance original) throws NullArgumentException {
        copy(original, this);
    }

    
{@inheritDoc}

If all values are available, it is more accurate to use evaluate(double[]) rather than adding values one at a time using this method and then executing getResult, since evaluate leverages the fact that is has the full list of values together to execute a two-pass algorithm. See Variance.


Note also that when Variance(SecondMoment) is used to create a Variance, this method does nothing. In that case, the SecondMoment should be incremented directly.


/**
     * {@inheritDoc}
     * <p>If all values are available, it is more accurate to use
     * {@link #evaluate(double[])} rather than adding values one at a time
     * using this method and then executing {@link #getResult}, since
     * <code>evaluate</code> leverages the fact that is has the full
     * list of values together to execute a two-pass algorithm.
     * See {@link Variance}.</p>
     *
     * <p>Note also that when {@link #Variance(SecondMoment)} is used to
     * create a Variance, this method does nothing. In that case, the
     * SecondMoment should be incremented directly.</p>
     */
    @Override
    public void increment(final double d) {
        if (incMoment) {
            moment.increment(d);
        }
    }

    
{@inheritDoc}

/**
     * {@inheritDoc}
     */
    @Override
    public double getResult() {
            if (moment.n == 0) {
                return Double.NaN;
            } else if (moment.n == 1) {
                return 0d;
            } else {
                if (isBiasCorrected) {
                    return moment.m2 / (moment.n - 1d);
                } else {
                    return moment.m2 / (moment.n);
                }
            }
    }

    
{@inheritDoc}

/**
     * {@inheritDoc}
     */
    public long getN() {
        return moment.getN();
    }

    
{@inheritDoc}

/**
     * {@inheritDoc}
     */
    @Override
    public void clear() {
        if (incMoment) {
            moment.clear();
        }
    }

    
Returns the variance of the entries in the input array, or
Double.NaN if the array is empty.

 See Variance for details on the computing algorithm.



Returns 0 for a single-value (i.e. length = 1) sample.



Throws MathIllegalArgumentException if the array is null.



Does not change the internal state of the statistic.


Params:
  • values – the input array
Throws:
Returns:the variance of the values or Double.NaN if length = 0
/**
     * Returns the variance of the entries in the input array, or
     * <code>Double.NaN</code> if the array is empty.
     * <p>
     * See {@link Variance} for details on the computing algorithm.</p>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if the array is null.</p>
     * <p>
     * Does not change the internal state of the statistic.</p>
     *
     * @param values the input array
     * @return the variance of the values or Double.NaN if length = 0
     * @throws MathIllegalArgumentException if the array is null
     */
    @Override
    public double evaluate(final double[] values) throws MathIllegalArgumentException {
        if (values == null) {
            throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
        }
        return evaluate(values, 0, values.length);
    }

    
Returns the variance of the entries in the specified portion of
the input array, or Double.NaN if the designated subarray
is empty.  Note that Double.NaN may also be returned if the input
includes NaN and / or infinite values.

 See Variance for details on the computing algorithm.



Returns 0 for a single-value (i.e. length = 1) sample.



Does not change the internal state of the statistic.



Throws MathIllegalArgumentException if the array is null.


Params:
  • values – the input array
  • begin – index of the first array element to include
  • length – the number of elements to include
Throws:
Returns:the variance of the values or Double.NaN if length = 0
/**
     * Returns the variance of the entries in the specified portion of
     * the input array, or <code>Double.NaN</code> if the designated subarray
     * is empty.  Note that Double.NaN may also be returned if the input
     * includes NaN and / or infinite values.
     * <p>
     * See {@link Variance} for details on the computing algorithm.</p>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Does not change the internal state of the statistic.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if the array is null.</p>
     *
     * @param values the input array
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the variance of the values or Double.NaN if length = 0
     * @throws MathIllegalArgumentException if the array is null or the array index
     *  parameters are not valid
     */
    @Override
    public double evaluate(final double[] values, final int begin, final int length)
    throws MathIllegalArgumentException {

        double var = Double.NaN;

        if (test(values, begin, length)) {
            clear();
            if (length == 1) {
                var = 0.0;
            } else if (length > 1) {
                Mean mean = new Mean();
                double m = mean.evaluate(values, begin, length);
                var = evaluate(values, m, begin, length);
            }
        }
        return var;
    }

    
Returns the weighted variance of the entries in the specified portion of
the input array, or Double.NaN if the designated subarray
is empty.



Uses the formula 
  Σ(weights[i]*(values[i] - weightedMean)2)/(Σ(weights[i]) - 1)


where weightedMean is the weighted mean



This formula will not return the same result as the unweighted variance when all
weights are equal, unless all weights are equal to 1. The formula assumes that
weights are to be treated as "expansion values," as will be the case if for example
the weights represent frequency counts. To normalize weights so that the denominator
in the variance computation equals the length of the input vector minus one, use 
  evaluate(values, MathArrays.normalizeArray(weights, values.length)); 




Returns 0 for a single-value (i.e. length = 1) sample.



Throws IllegalArgumentException if any of the following are true:

  • the values array is null
    • 
    
  • the weights array is null
    • 
    
  • the weights array does not have the same length as the values array
    • 
    
  • the weights array contains one or more infinite values
    • 
    
  • the weights array contains one or more NaN values
    • 
    
  • the weights array contains negative values
    • 
    
  • the start and length arguments do not determine a valid array
    • 




Does not change the internal state of the statistic.



Throws MathIllegalArgumentException if either array is null.


Params:
  • values – the input array
  • weights – the weights array
  • begin – index of the first array element to include
  • length – the number of elements to include
Throws:
Returns:the weighted variance of the values or Double.NaN if length = 0
Since:2.1
/**
     * <p>Returns the weighted variance of the entries in the specified portion of
     * the input array, or <code>Double.NaN</code> if the designated subarray
     * is empty.</p>
     * <p>
     * Uses the formula <pre>
     *   &Sigma;(weights[i]*(values[i] - weightedMean)<sup>2</sup>)/(&Sigma;(weights[i]) - 1)
     * </pre>
     * where weightedMean is the weighted mean</p>
     * <p>
     * This formula will not return the same result as the unweighted variance when all
     * weights are equal, unless all weights are equal to 1. The formula assumes that
     * weights are to be treated as "expansion values," as will be the case if for example
     * the weights represent frequency counts. To normalize weights so that the denominator
     * in the variance computation equals the length of the input vector minus one, use <pre>
     *   <code>evaluate(values, MathArrays.normalizeArray(weights, values.length)); </code>
     * </pre>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>IllegalArgumentException</code> if any of the following are true:
     * <ul><li>the values array is null</li>
     *     <li>the weights array is null</li>
     *     <li>the weights array does not have the same length as the values array</li>
     *     <li>the weights array contains one or more infinite values</li>
     *     <li>the weights array contains one or more NaN values</li>
     *     <li>the weights array contains negative values</li>
     *     <li>the start and length arguments do not determine a valid array</li>
     * </ul></p>
     * <p>
     * Does not change the internal state of the statistic.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if either array is null.</p>
     *
     * @param values the input array
     * @param weights the weights array
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the weighted variance of the values or Double.NaN if length = 0
     * @throws MathIllegalArgumentException if the parameters are not valid
     * @since 2.1
     */
    public double evaluate(final double[] values, final double[] weights,
                           final int begin, final int length) throws MathIllegalArgumentException {

        double var = Double.NaN;

        if (test(values, weights,begin, length)) {
            clear();
            if (length == 1) {
                var = 0.0;
            } else if (length > 1) {
                Mean mean = new Mean();
                double m = mean.evaluate(values, weights, begin, length);
                var = evaluate(values, weights, m, begin, length);
            }
        }
        return var;
    }

    

Returns the weighted variance of the entries in the the input array.



Uses the formula 
  Σ(weights[i]*(values[i] - weightedMean)2)/(Σ(weights[i]) - 1)


where weightedMean is the weighted mean



This formula will not return the same result as the unweighted variance when all
weights are equal, unless all weights are equal to 1. The formula assumes that
weights are to be treated as "expansion values," as will be the case if for example
the weights represent frequency counts. To normalize weights so that the denominator
in the variance computation equals the length of the input vector minus one, use 
  evaluate(values, MathArrays.normalizeArray(weights, values.length)); 




Returns 0 for a single-value (i.e. length = 1) sample.



Throws MathIllegalArgumentException if any of the following are true:

  • the values array is null
    • 
    
  • the weights array is null
    • 
    
  • the weights array does not have the same length as the values array
    • 
    
  • the weights array contains one or more infinite values
    • 
    
  • the weights array contains one or more NaN values
    • 
    
  • the weights array contains negative values
    • 




Does not change the internal state of the statistic.



Throws MathIllegalArgumentException if either array is null.


Params:
  • values – the input array
  • weights – the weights array
Throws:
Returns:the weighted variance of the values
Since:2.1
/**
     * <p>
     * Returns the weighted variance of the entries in the the input array.</p>
     * <p>
     * Uses the formula <pre>
     *   &Sigma;(weights[i]*(values[i] - weightedMean)<sup>2</sup>)/(&Sigma;(weights[i]) - 1)
     * </pre>
     * where weightedMean is the weighted mean</p>
     * <p>
     * This formula will not return the same result as the unweighted variance when all
     * weights are equal, unless all weights are equal to 1. The formula assumes that
     * weights are to be treated as "expansion values," as will be the case if for example
     * the weights represent frequency counts. To normalize weights so that the denominator
     * in the variance computation equals the length of the input vector minus one, use <pre>
     *   <code>evaluate(values, MathArrays.normalizeArray(weights, values.length)); </code>
     * </pre>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if any of the following are true:
     * <ul><li>the values array is null</li>
     *     <li>the weights array is null</li>
     *     <li>the weights array does not have the same length as the values array</li>
     *     <li>the weights array contains one or more infinite values</li>
     *     <li>the weights array contains one or more NaN values</li>
     *     <li>the weights array contains negative values</li>
     * </ul></p>
     * <p>
     * Does not change the internal state of the statistic.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if either array is null.</p>
     *
     * @param values the input array
     * @param weights the weights array
     * @return the weighted variance of the values
     * @throws MathIllegalArgumentException if the parameters are not valid
     * @since 2.1
     */
    public double evaluate(final double[] values, final double[] weights)
    throws MathIllegalArgumentException {
        return evaluate(values, weights, 0, values.length);
    }

    
Returns the variance of the entries in the specified portion of
the input array, using the precomputed mean value.  Returns
Double.NaN if the designated subarray is empty.

 See Variance for details on the computing algorithm.



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.



Returns 0 for a single-value (i.e. length = 1) sample.



Throws MathIllegalArgumentException if the array is null.



Does not change the internal state of the statistic.


Params:
  • values – the input array
  • mean – the precomputed mean value
  • begin – index of the first array element to include
  • length – the number of elements to include
Throws:
Returns:the variance of the values or Double.NaN if length = 0
/**
     * Returns the variance of the entries in the specified portion of
     * the input array, using the precomputed mean value.  Returns
     * <code>Double.NaN</code> if the designated subarray is empty.
     * <p>
     * See {@link Variance} for details on the computing algorithm.</p>
     * <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.</p>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if the array is null.</p>
     * <p>
     * Does not change the internal state of the statistic.</p>
     *
     * @param values the input array
     * @param mean the precomputed mean value
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the variance of the values or Double.NaN if length = 0
     * @throws MathIllegalArgumentException if the array is null or the array index
     *  parameters are not valid
     */
    public double evaluate(final double[] values, final double mean,
            final int begin, final int length) throws MathIllegalArgumentException {

        double var = Double.NaN;

        if (test(values, begin, length)) {
            if (length == 1) {
                var = 0.0;
            } else if (length > 1) {
                double accum = 0.0;
                double dev = 0.0;
                double accum2 = 0.0;
                for (int i = begin; i < begin + length; i++) {
                    dev = values[i] - mean;
                    accum += dev * dev;
                    accum2 += dev;
                }
                double len = length;
                if (isBiasCorrected) {
                    var = (accum - (accum2 * accum2 / len)) / (len - 1.0);
                } else {
                    var = (accum - (accum2 * accum2 / len)) / len;
                }
            }
        }
        return var;
    }

    
Returns the variance of the entries in the input array, using the
precomputed mean value.  Returns Double.NaN if the array
is empty.

 See Variance for details on the computing algorithm.



If isBiasCorrected is true 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 isBiasCorrected to false before
invoking this method.



Returns 0 for a single-value (i.e. length = 1) sample.



Throws MathIllegalArgumentException if the array is null.



Does not change the internal state of the statistic.


Params:
  • values – the input array
  • mean – the precomputed mean value
Throws:
Returns:the variance of the values or Double.NaN if the array is empty
/**
     * Returns the variance of the entries in the input array, using the
     * precomputed mean value.  Returns <code>Double.NaN</code> if the array
     * is empty.
     * <p>
     * See {@link Variance} for details on the computing algorithm.</p>
     * <p>
     * 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>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if the array is null.</p>
     * <p>
     * Does not change the internal state of the statistic.</p>
     *
     * @param values the input array
     * @param mean the precomputed mean value
     * @return the variance of the values or Double.NaN if the array is empty
     * @throws MathIllegalArgumentException if the array is null
     */
    public double evaluate(final double[] values, final double mean) throws MathIllegalArgumentException {
        return evaluate(values, mean, 0, values.length);
    }

    
Returns the weighted variance of the entries in the specified portion of
the input array, using the precomputed weighted mean value.  Returns
Double.NaN if the designated subarray is empty.


Uses the formula 
  Σ(weights[i]*(values[i] - mean)2)/(Σ(weights[i]) - 1)




The formula used assumes that the supplied mean value is the weighted 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.



This formula will not return the same result as the unweighted variance when all
weights are equal, unless all weights are equal to 1. The formula assumes that
weights are to be treated as "expansion values," as will be the case if for example
the weights represent frequency counts. To normalize weights so that the denominator
in the variance computation equals the length of the input vector minus one, use 
  evaluate(values, MathArrays.normalizeArray(weights, values.length), mean); 




Returns 0 for a single-value (i.e. length = 1) sample.



Throws MathIllegalArgumentException if any of the following are true:

  • the values array is null
    • 
    
  • the weights array is null
    • 
    
  • the weights array does not have the same length as the values array
    • 
    
  • the weights array contains one or more infinite values
    • 
    
  • the weights array contains one or more NaN values
    • 
    
  • the weights array contains negative values
    • 
    
  • the start and length arguments do not determine a valid array
    • 




Does not change the internal state of the statistic.


Params:
  • values – the input array
  • weights – the weights array
  • mean – the precomputed weighted mean value
  • begin – index of the first array element to include
  • length – the number of elements to include
Throws:
Returns:the variance of the values or Double.NaN if length = 0
Since:2.1
/**
     * Returns the weighted variance of the entries in the specified portion of
     * the input array, using the precomputed weighted mean value.  Returns
     * <code>Double.NaN</code> if the designated subarray is empty.
     * <p>
     * Uses the formula <pre>
     *   &Sigma;(weights[i]*(values[i] - mean)<sup>2</sup>)/(&Sigma;(weights[i]) - 1)
     * </pre></p>
     * <p>
     * The formula used assumes that the supplied mean value is the weighted 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.</p>
     * <p>
     * This formula will not return the same result as the unweighted variance when all
     * weights are equal, unless all weights are equal to 1. The formula assumes that
     * weights are to be treated as "expansion values," as will be the case if for example
     * the weights represent frequency counts. To normalize weights so that the denominator
     * in the variance computation equals the length of the input vector minus one, use <pre>
     *   <code>evaluate(values, MathArrays.normalizeArray(weights, values.length), mean); </code>
     * </pre>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if any of the following are true:
     * <ul><li>the values array is null</li>
     *     <li>the weights array is null</li>
     *     <li>the weights array does not have the same length as the values array</li>
     *     <li>the weights array contains one or more infinite values</li>
     *     <li>the weights array contains one or more NaN values</li>
     *     <li>the weights array contains negative values</li>
     *     <li>the start and length arguments do not determine a valid array</li>
     * </ul></p>
     * <p>
     * Does not change the internal state of the statistic.</p>
     *
     * @param values the input array
     * @param weights the weights array
     * @param mean the precomputed weighted mean value
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the variance of the values or Double.NaN if length = 0
     * @throws MathIllegalArgumentException if the parameters are not valid
     * @since 2.1
     */
    public double evaluate(final double[] values, final double[] weights,
    final double mean, final int begin, final int length)
    throws MathIllegalArgumentException {

        double var = Double.NaN;

        if (test(values, weights, begin, length)) {
            if (length == 1) {
                var = 0.0;
            } else if (length > 1) {
                double accum = 0.0;
                double dev = 0.0;
                double accum2 = 0.0;
                for (int i = begin; i < begin + length; i++) {
                    dev = values[i] - mean;
                    accum += weights[i] * (dev * dev);
                    accum2 += weights[i] * dev;
                }

                double sumWts = 0;
                for (int i = begin; i < begin + length; i++) {
                    sumWts += weights[i];
                }

                if (isBiasCorrected) {
                    var = (accum - (accum2 * accum2 / sumWts)) / (sumWts - 1.0);
                } else {
                    var = (accum - (accum2 * accum2 / sumWts)) / sumWts;
                }
            }
        }
        return var;
    }

    
Returns the weighted variance of the values in the input array, using
the precomputed weighted mean value.



Uses the formula 
  Σ(weights[i]*(values[i] - mean)2)/(Σ(weights[i]) - 1)




The formula used assumes that the supplied mean value is the weighted 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.



This formula will not return the same result as the unweighted variance when all
weights are equal, unless all weights are equal to 1. The formula assumes that
weights are to be treated as "expansion values," as will be the case if for example
the weights represent frequency counts. To normalize weights so that the denominator
in the variance computation equals the length of the input vector minus one, use 
  evaluate(values, MathArrays.normalizeArray(weights, values.length), mean); 




Returns 0 for a single-value (i.e. length = 1) sample.



Throws MathIllegalArgumentException if any of the following are true:

  • the values array is null
    • 
    
  • the weights array is null
    • 
    
  • the weights array does not have the same length as the values array
    • 
    
  • the weights array contains one or more infinite values
    • 
    
  • the weights array contains one or more NaN values
    • 
    
  • the weights array contains negative values
    • 




Does not change the internal state of the statistic.


Params:
  • values – the input array
  • weights – the weights array
  • mean – the precomputed weighted mean value
Throws:
Returns:the variance of the values or Double.NaN if length = 0
Since:2.1
/**
     * <p>Returns the weighted variance of the values in the input array, using
     * the precomputed weighted mean value.</p>
     * <p>
     * Uses the formula <pre>
     *   &Sigma;(weights[i]*(values[i] - mean)<sup>2</sup>)/(&Sigma;(weights[i]) - 1)
     * </pre></p>
     * <p>
     * The formula used assumes that the supplied mean value is the weighted 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.</p>
     * <p>
     * This formula will not return the same result as the unweighted variance when all
     * weights are equal, unless all weights are equal to 1. The formula assumes that
     * weights are to be treated as "expansion values," as will be the case if for example
     * the weights represent frequency counts. To normalize weights so that the denominator
     * in the variance computation equals the length of the input vector minus one, use <pre>
     *   <code>evaluate(values, MathArrays.normalizeArray(weights, values.length), mean); </code>
     * </pre>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>MathIllegalArgumentException</code> if any of the following are true:
     * <ul><li>the values array is null</li>
     *     <li>the weights array is null</li>
     *     <li>the weights array does not have the same length as the values array</li>
     *     <li>the weights array contains one or more infinite values</li>
     *     <li>the weights array contains one or more NaN values</li>
     *     <li>the weights array contains negative values</li>
     * </ul></p>
     * <p>
     * Does not change the internal state of the statistic.</p>
     *
     * @param values the input array
     * @param weights the weights array
     * @param mean the precomputed weighted mean value
     * @return the variance of the values or Double.NaN if length = 0
     * @throws MathIllegalArgumentException if the parameters are not valid
     * @since 2.1
     */
    public double evaluate(final double[] values, final double[] weights, final double mean)
    throws MathIllegalArgumentException {
        return evaluate(values, weights, mean, 0, values.length);
    }

    
Returns:Returns the isBiasCorrected.
/**
     * @return Returns the isBiasCorrected.
     */
    public boolean isBiasCorrected() {
        return isBiasCorrected;
    }

    
Params:
  • biasCorrected – The isBiasCorrected to set.
/**
     * @param biasCorrected The isBiasCorrected to set.
     */
    public void setBiasCorrected(boolean biasCorrected) {
        this.isBiasCorrected = biasCorrected;
    }

    
{@inheritDoc}

/**
     * {@inheritDoc}
     */
    @Override
    public Variance copy() {
        Variance result = new Variance();
        // No try-catch or advertised exception because parameters are guaranteed non-null
        copy(this, result);
        return result;
    }

    
Copies source to dest.

Neither source nor dest can be null.


Params:
  • source – Variance to copy
  • dest – Variance to copy to
Throws:
/**
     * Copies source to dest.
     * <p>Neither source nor dest can be null.</p>
     *
     * @param source Variance to copy
     * @param dest Variance to copy to
     * @throws NullArgumentException if either source or dest is null
     */
    public static void copy(Variance source, Variance dest)
        throws NullArgumentException {
        MathUtils.checkNotNull(source);
        MathUtils.checkNotNull(dest);
        dest.setData(source.getDataRef());
        dest.moment = source.moment.copy();
        dest.isBiasCorrected = source.isBiasCorrected;
        dest.incMoment = source.incMoment;
    }
}