/**
* 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));
}
}