com.opengamma.strata.math.impl.statistics.descriptive.SampleSkewnessCalculator Maven / Gradle / Ivy

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

import java.util.function.Function;

import com.opengamma.strata.collect.ArgChecker;

/**
 * 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 implements Function {

  private static final Function MEAN = new MeanCalculator();

  @Override
  public Double apply(double[] x) {
    ArgChecker.notNull(x, "x");
    ArgChecker.isTrue(x.length >= 3, "Need at least three points to calculate sample skewness");
    double sum = 0;
    double variance = 0;
    double mean = MEAN.apply(x);
    for (double d : x) {
      double diff = d - mean;
      variance += diff * diff;
      sum += diff * diff * diff;
    }
    int n = x.length;
    variance /= n - 1;
    return Math.sqrt(n - 1.) * sum / (Math.pow(variance, 1.5) * Math.sqrt(n) * (n - 2));
  }

}