com.opengamma.analytics.math.statistics.descriptive.SampleSkewnessCalculator.java Source code

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Here is the source code for com.opengamma.analytics.math.statistics.descriptive.SampleSkewnessCalculator.java

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/**
 * Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
 * 
 * Please see distribution for license.
 */
package com.opengamma.analytics.math.statistics.descriptive;

import org.apache.commons.lang.Validate;

import com.opengamma.analytics.math.function.Function1D;

/**
 * The sample skewness gives a measure of the asymmetry of the probability
 * distribution of a variable. For a series of data $x_1, x_2, \dots, x_n$, an
 * unbiased estimator of the sample skewness is
 * $$
 * \begin{align*}
 * \mu_3 = \frac{\sqrt{n(n-1)}}{n-2}\frac{\frac{1}{n}\sum_{i=1}^n (x_i - \overline{x})^3}{\left(\frac{1}{n}\sum_{i=1}^n (x_i - \overline{x})^2\right)^\frac{3}{2}}
 * \end{align*}
 * $$
 * where $\overline{x}$ is the sample mean.
 */
public class SampleSkewnessCalculator extends Function1D<double[], Double> {
    private static final Function1D<double[], Double> MEAN = new MeanCalculator();

    /**
     * @param x The array of data, not null, must contain at least three data points
     * @return The sample skewness
     */
    @Override
    public Double evaluate(final double[] x) {
        Validate.notNull(x, "x");
        Validate.isTrue(x.length >= 3, "Need at least three points to calculate sample skewness");
        double sum = 0;
        double variance = 0;
        final double mean = MEAN.evaluate(x);
        for (final Double d : x) {
            final double diff = d - mean;
            variance += diff * diff;
            sum += diff * diff * diff;
        }
        final int n = x.length;
        variance /= n - 1;
        return Math.sqrt(n - 1.) * sum / (Math.pow(variance, 1.5) * Math.sqrt(n) * (n - 2));
    }

}