Java tutorial
/* * 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; import org.apache.commons.math3.exception.MathIllegalArgumentException; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.exception.DimensionMismatchException; import org.apache.commons.math3.exception.NoDataException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.stat.descriptive.DescriptiveStatistics; import org.apache.commons.math3.stat.descriptive.UnivariateStatistic; import org.apache.commons.math3.stat.descriptive.moment.GeometricMean; import org.apache.commons.math3.stat.descriptive.moment.Mean; import org.apache.commons.math3.stat.descriptive.moment.Variance; import org.apache.commons.math3.stat.descriptive.rank.Max; import org.apache.commons.math3.stat.descriptive.rank.Min; import org.apache.commons.math3.stat.descriptive.rank.Percentile; import org.apache.commons.math3.stat.descriptive.summary.Product; import org.apache.commons.math3.stat.descriptive.summary.Sum; import org.apache.commons.math3.stat.descriptive.summary.SumOfLogs; import org.apache.commons.math3.stat.descriptive.summary.SumOfSquares; /** * StatUtils provides static methods for computing statistics based on data * stored in double[] arrays. * * @version $Id: StatUtils.java 1416643 2012-12-03 19:37:14Z tn $ */ public final class StatUtils { /** sum */ private static final UnivariateStatistic SUM = new Sum(); /** sumSq */ private static final UnivariateStatistic SUM_OF_SQUARES = new SumOfSquares(); /** prod */ private static final UnivariateStatistic PRODUCT = new Product(); /** sumLog */ private static final UnivariateStatistic SUM_OF_LOGS = new SumOfLogs(); /** min */ private static final UnivariateStatistic MIN = new Min(); /** max */ private static final UnivariateStatistic MAX = new Max(); /** mean */ private static final UnivariateStatistic MEAN = new Mean(); /** variance */ private static final Variance VARIANCE = new Variance(); /** percentile */ private static final Percentile PERCENTILE = new Percentile(); /** geometric mean */ private static final GeometricMean GEOMETRIC_MEAN = new GeometricMean(); /** * Private Constructor */ private StatUtils() { } /** * Returns the sum of the values in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * Throws <code>IllegalArgumentException</code> if the input array * is null.</p> * * @param values array of values to sum * @return the sum of the values or <code>Double.NaN</code> if the array * is empty * @throws MathIllegalArgumentException if the array is null */ public static double sum(final double[] values) throws MathIllegalArgumentException { return SUM.evaluate(values); } /** * Returns the sum of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * Throws <code>IllegalArgumentException</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 sum 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 static double sum(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return SUM.evaluate(values, begin, length); } /** * Returns the sum of the squares of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * Throws <code>IllegalArgumentException</code> if the array is null.</p> * * @param values input array * @return the sum of the squared values or <code>Double.NaN</code> if the * array is empty * @throws MathIllegalArgumentException if the array is null */ public static double sumSq(final double[] values) throws MathIllegalArgumentException { return SUM_OF_SQUARES.evaluate(values); } /** * Returns the sum of the squares of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * Throws <code>IllegalArgumentException</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 sum of the squares 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 static double sumSq(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return SUM_OF_SQUARES.evaluate(values, begin, length); } /** * Returns the product of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * Throws <code>IllegalArgumentException</code> if the array is null.</p> * * @param values the input array * @return the product of the values or Double.NaN if the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double product(final double[] values) throws MathIllegalArgumentException { return PRODUCT.evaluate(values); } /** * Returns the product of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * Throws <code>IllegalArgumentException</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 product 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 static double product(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return PRODUCT.evaluate(values, begin, length); } /** * Returns the sum of the natural logs of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * Throws <code>IllegalArgumentException</code> if the array is null.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.summary.SumOfLogs}. * </p> * * @param values the input array * @return the sum of the natural logs of the values or Double.NaN if * the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double sumLog(final double[] values) throws MathIllegalArgumentException { return SUM_OF_LOGS.evaluate(values); } /** * Returns the sum of the natural logs of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * Throws <code>IllegalArgumentException</code> if the array is null.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.summary.SumOfLogs}. * </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 sum of the natural logs 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 static double sumLog(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return SUM_OF_LOGS.evaluate(values, begin, length); } /** * Returns the arithmetic mean of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * Throws <code>IllegalArgumentException</code> if the array is null.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.Mean} for * details on the computing algorithm.</p> * * @param values the input array * @return the mean of the values or Double.NaN if the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double mean(final double[] values) throws MathIllegalArgumentException { return MEAN.evaluate(values); } /** * Returns the arithmetic mean of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * Throws <code>IllegalArgumentException</code> if the array is null.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.Mean} for * details on the computing algorithm.</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 mean 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 static double mean(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return MEAN.evaluate(values, begin, length); } /** * Returns the geometric mean of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * Throws <code>IllegalArgumentException</code> if the array is null.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.GeometricMean} * for details on the computing algorithm.</p> * * @param values the input array * @return the geometric mean of the values or Double.NaN if the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double geometricMean(final double[] values) throws MathIllegalArgumentException { return GEOMETRIC_MEAN.evaluate(values); } /** * Returns the geometric mean of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * Throws <code>IllegalArgumentException</code> if the array is null.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.GeometricMean} * for details on the computing algorithm.</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 geometric mean 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 static double geometricMean(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return GEOMETRIC_MEAN.evaluate(values, begin, length); } /** * Returns the variance of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * * <p>This method returns the bias-corrected sample variance (using {@code n - 1} in * the denominator). Use {@link #populationVariance(double[])} for the non-bias-corrected * population variance.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.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> * * @param values the input array * @return the variance of the values or Double.NaN if the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double variance(final double[] values) throws MathIllegalArgumentException { return VARIANCE.evaluate(values); } /** * 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. * * <p>This method returns the bias-corrected sample variance (using {@code n - 1} in * the denominator). Use {@link #populationVariance(double[], int, int)} for the non-bias-corrected * population variance.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.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 or the * array index parameters are not valid.</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 */ public static double variance(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return VARIANCE.evaluate(values, begin, length); } /** * 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>This method returns the bias-corrected sample variance (using {@code n - 1} in * the denominator). Use {@link #populationVariance(double[], double, int, int)} for the non-bias-corrected * population variance.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.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 or the * array index parameters are not valid.</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 static double variance(final double[] values, final double mean, final int begin, final int length) throws MathIllegalArgumentException { return VARIANCE.evaluate(values, mean, begin, length); } /** * 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>This method returns the bias-corrected sample variance (using {@code n - 1} in * the denominator). Use {@link #populationVariance(double[], double)} for the non-bias-corrected * population variance.</p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.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> * * @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 static double variance(final double[] values, final double mean) throws MathIllegalArgumentException { return VARIANCE.evaluate(values, mean); } /** * Returns the <a href="http://en.wikibooks.org/wiki/Statistics/Summary/Variance"> * population variance</a> of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.Variance} for * details on the formula and 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> * * @param values the input array * @return the population variance of the values or Double.NaN if the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double populationVariance(final double[] values) throws MathIllegalArgumentException { return new Variance(false).evaluate(values); } /** * Returns the <a href="http://en.wikibooks.org/wiki/Statistics/Summary/Variance"> * population variance</a> of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * See {@link org.apache.commons.math3.stat.descriptive.moment.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 or the * array index parameters are not valid.</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 population 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 static double populationVariance(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return new Variance(false).evaluate(values, begin, length); } /** * Returns the <a href="http://en.wikibooks.org/wiki/Statistics/Summary/Variance"> * population variance</a> 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 org.apache.commons.math3.stat.descriptive.moment.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 or the * array index parameters are not valid.</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 population 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 static double populationVariance(final double[] values, final double mean, final int begin, final int length) throws MathIllegalArgumentException { return new Variance(false).evaluate(values, mean, begin, length); } /** * Returns the <a href="http://en.wikibooks.org/wiki/Statistics/Summary/Variance"> * population variance</a> 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 org.apache.commons.math3.stat.descriptive.moment.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> * * @param values the input array * @param mean the precomputed mean value * @return the population variance of the values or Double.NaN if the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double populationVariance(final double[] values, final double mean) throws MathIllegalArgumentException { return new Variance(false).evaluate(values, mean); } /** * Returns the maximum of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * Throws <code>MathIllegalArgumentException</code> if the array is null.</p> * <p> * <ul> * <li>The result is <code>NaN</code> iff all values are <code>NaN</code> * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li> * <li>If any of the values equals <code>Double.POSITIVE_INFINITY</code>, * the result is <code>Double.POSITIVE_INFINITY.</code></li> * </ul></p> * * @param values the input array * @return the maximum of the values or Double.NaN if the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double max(final double[] values) throws MathIllegalArgumentException { return MAX.evaluate(values); } /** * Returns the maximum of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * Throws <code>MathIllegalArgumentException</code> if the array is null or * the array index parameters are not valid.</p> * <p> * <ul> * <li>The result is <code>NaN</code> iff all values are <code>NaN</code> * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li> * <li>If any of the values equals <code>Double.POSITIVE_INFINITY</code>, * the result is <code>Double.POSITIVE_INFINITY.</code></li> * </ul></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 maximum 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 static double max(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return MAX.evaluate(values, begin, length); } /** * Returns the minimum of the entries in the input array, or * <code>Double.NaN</code> if the array is empty. * <p> * Throws <code>MathIllegalArgumentException</code> if the array is null.</p> * <p> * <ul> * <li>The result is <code>NaN</code> iff all values are <code>NaN</code> * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li> * <li>If any of the values equals <code>Double.NEGATIVE_INFINITY</code>, * the result is <code>Double.NEGATIVE_INFINITY.</code></li> * </ul> </p> * * @param values the input array * @return the minimum of the values or Double.NaN if the array is empty * @throws MathIllegalArgumentException if the array is null */ public static double min(final double[] values) throws MathIllegalArgumentException { return MIN.evaluate(values); } /** * Returns the minimum of the entries in the specified portion of * the input array, or <code>Double.NaN</code> if the designated subarray * is empty. * <p> * Throws <code>MathIllegalArgumentException</code> if the array is null or * the array index parameters are not valid.</p> * <p> * <ul> * <li>The result is <code>NaN</code> iff all values are <code>NaN</code> * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li> * <li>If any of the values equals <code>Double.NEGATIVE_INFINITY</code>, * the result is <code>Double.NEGATIVE_INFINITY.</code></li> * </ul></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 minimum 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 static double min(final double[] values, final int begin, final int length) throws MathIllegalArgumentException { return MIN.evaluate(values, begin, length); } /** * Returns an estimate of the <code>p</code>th percentile of the values * in the <code>values</code> array. * <p> * <ul> * <li>Returns <code>Double.NaN</code> if <code>values</code> has length * <code>0</code></li></p> * <li>Returns (for any value of <code>p</code>) <code>values[0]</code> * if <code>values</code> has length <code>1</code></li> * <li>Throws <code>IllegalArgumentException</code> if <code>values</code> * is null or p is not a valid quantile value (p must be greater than 0 * and less than or equal to 100)</li> * </ul></p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.rank.Percentile} for * a description of the percentile estimation algorithm used.</p> * * @param values input array of values * @param p the percentile value to compute * @return the percentile value or Double.NaN if the array is empty * @throws MathIllegalArgumentException if <code>values</code> is null * or p is invalid */ public static double percentile(final double[] values, final double p) throws MathIllegalArgumentException { return PERCENTILE.evaluate(values, p); } /** * Returns an estimate of the <code>p</code>th percentile of the values * in the <code>values</code> array, starting with the element in (0-based) * position <code>begin</code> in the array and including <code>length</code> * values. * <p> * <ul> * <li>Returns <code>Double.NaN</code> if <code>length = 0</code></li> * <li>Returns (for any value of <code>p</code>) <code>values[begin]</code> * if <code>length = 1 </code></li> * <li>Throws <code>MathIllegalArgumentException</code> if <code>values</code> * is null , <code>begin</code> or <code>length</code> is invalid, or * <code>p</code> is not a valid quantile value (p must be greater than 0 * and less than or equal to 100)</li> * </ul></p> * <p> * See {@link org.apache.commons.math3.stat.descriptive.rank.Percentile} for * a description of the percentile estimation algorithm used.</p> * * @param values array of input values * @param p the percentile to compute * @param begin the first (0-based) element to include in the computation * @param length the number of array elements to include * @return the percentile value * @throws MathIllegalArgumentException if the parameters are not valid or the * input array is null */ public static double percentile(final double[] values, final int begin, final int length, final double p) throws MathIllegalArgumentException { return PERCENTILE.evaluate(values, begin, length, p); } /** * Returns the sum of the (signed) differences between corresponding elements of the * input arrays -- i.e., sum(sample1[i] - sample2[i]). * * @param sample1 the first array * @param sample2 the second array * @return sum of paired differences * @throws DimensionMismatchException if the arrays do not have the same * (positive) length. * @throws NoDataException if the sample arrays are empty. */ public static double sumDifference(final double[] sample1, final double[] sample2) throws DimensionMismatchException, NoDataException { int n = sample1.length; if (n != sample2.length) { throw new DimensionMismatchException(n, sample2.length); } if (n <= 0) { throw new NoDataException(LocalizedFormats.INSUFFICIENT_DIMENSION); } double result = 0; for (int i = 0; i < n; i++) { result += sample1[i] - sample2[i]; } return result; } /** * Returns the mean of the (signed) differences between corresponding elements of the * input arrays -- i.e., sum(sample1[i] - sample2[i]) / sample1.length. * * @param sample1 the first array * @param sample2 the second array * @return mean of paired differences * @throws DimensionMismatchException if the arrays do not have the same * (positive) length. * @throws NoDataException if the sample arrays are empty. */ public static double meanDifference(final double[] sample1, final double[] sample2) throws DimensionMismatchException, NoDataException { return sumDifference(sample1, sample2) / sample1.length; } /** * Returns the variance of the (signed) differences between corresponding elements of the * input arrays -- i.e., var(sample1[i] - sample2[i]). * * @param sample1 the first array * @param sample2 the second array * @param meanDifference the mean difference between corresponding entries * @see #meanDifference(double[],double[]) * @return variance of paired differences * @throws DimensionMismatchException if the arrays do not have the same * length. * @throws NumberIsTooSmallException if the arrays length is less than 2. */ public static double varianceDifference(final double[] sample1, final double[] sample2, double meanDifference) throws DimensionMismatchException, NumberIsTooSmallException { double sum1 = 0d; double sum2 = 0d; double diff = 0d; int n = sample1.length; if (n != sample2.length) { throw new DimensionMismatchException(n, sample2.length); } if (n < 2) { throw new NumberIsTooSmallException(n, 2, true); } for (int i = 0; i < n; i++) { diff = sample1[i] - sample2[i]; sum1 += (diff - meanDifference) * (diff - meanDifference); sum2 += diff - meanDifference; } return (sum1 - (sum2 * sum2 / n)) / (n - 1); } /** * Normalize (standardize) the sample, so it is has a mean of 0 and a standard deviation of 1. * * @param sample Sample to normalize. * @return normalized (standardized) sample. * @since 2.2 */ public static double[] normalize(final double[] sample) { DescriptiveStatistics stats = new DescriptiveStatistics(); // Add the data from the series to stats for (int i = 0; i < sample.length; i++) { stats.addValue(sample[i]); } // Compute mean and standard deviation double mean = stats.getMean(); double standardDeviation = stats.getStandardDeviation(); // initialize the standardizedSample, which has the same length as the sample double[] standardizedSample = new double[sample.length]; for (int i = 0; i < sample.length; i++) { // z = (x- mean)/standardDeviation standardizedSample[i] = (sample[i] - mean) / standardDeviation; } return standardizedSample; } }