/// <summary>
/// Returns the sample coskewness between two arrays.
/// Arrays should be of equal length, and contain more than one element.
/// </summary>
/// <param name="arrayA"></param>
/// <param name="arrayB"></param>
/// <param name="coskewnessType"></param>
public static double Coskewness(double[] arrayA, double[] arrayB, CoskewnessType coskewnessType)
{
double m3 = ThirdCentralCrossMoment(arrayA, arrayB, coskewnessType);
double sd1 = StandardDeviation(arrayA);
double sd2 = StandardDeviation(arrayB);
if (coskewnessType == CoskewnessType.AAB)
return m3/(sd1*sd1*sd2);
return m3 / (sd1 * sd2 * sd2);
}
/// <summary>
/// Returns the sample coskewness between two arrays.
/// Arrays should be of equal length, and contain more than one element.
/// </summary>
/// <param name="arrayA"></param>
/// <param name="arrayB"></param>
/// <param name="coskewnessType"></param>
public static double Coskewness(double[] arrayA, double[] arrayB, CoskewnessType coskewnessType)
{
double m3 = ThirdCentralCrossMoment(arrayA, arrayB, coskewnessType);
double sd1 = StandardDeviation(arrayA);
double sd2 = StandardDeviation(arrayB);
if (coskewnessType == CoskewnessType.AAB)
{
return(m3 / (sd1 * sd1 * sd2));
}
return(m3 / (sd1 * sd2 * sd2));
}
/// <summary>
/// Returns the sample third central cross moment between two arrays.
/// Arrays should be of equal length, and contain more than one element.
/// </summary>
/// <param name="arrayA"></param>
/// <param name="arrayB"></param>
/// <param name="coskewnessType"></param>
private static double ThirdCentralCrossMoment(double[] arrayA, double[] arrayB, CoskewnessType coskewnessType)
{
if (arrayA.Length != arrayB.Length)
{
throw new ArgumentException("arrayA and arrayB should be the same length.");
}
int n = arrayA.Length;
double meanA = Mean(arrayA);
double meanB = Mean(arrayB);
double m3 = 0;
if (coskewnessType == CoskewnessType.AAB)
{
for (int i = 0; i < n; i++)
{
m3 += (arrayA[i] - meanA) * (arrayA[i] - meanA) * (arrayB[i] - meanB);
}
}
else
{
for (int i = 0; i < n; i++)
{
m3 += (arrayA[i] - meanA) * (arrayB[i] - meanB) * (arrayB[i] - meanB);
}
}
m3 *= n / ((n - 1.0) * (n - 2.0)); //because this is the sample coskew multiply by n/(n-1)(n-2) rather than 1/n
return(m3);
}
/// <summary>
/// Returns the sample third central cross moment between two arrays.
/// Arrays should be of equal length, and contain more than one element.
/// </summary>
/// <param name="arrayA"></param>
/// <param name="arrayB"></param>
/// <param name="coskewnessType"></param>
private static double ThirdCentralCrossMoment(double[] arrayA, double[] arrayB, CoskewnessType coskewnessType)
{
if(arrayA.Length != arrayB.Length)
throw new ArgumentException("arrayA and arrayB should be the same length.");
int n = arrayA.Length;
double meanA = Mean(arrayA);
double meanB = Mean(arrayB);
double m3 = 0;
if (coskewnessType == CoskewnessType.AAB)
{
for (int i = 0; i < n; i++)
m3 += (arrayA[i] - meanA) * (arrayA[i] - meanA) * (arrayB[i] - meanB);
}
else
{
for (int i = 0; i < n; i++)
m3 += (arrayA[i] - meanA) * (arrayB[i] - meanB) * (arrayB[i] - meanB);
}
m3 *= n / ((n - 1.0) * (n - 2.0)); //because this is the sample coskew multiply by n/(n-1)(n-2) rather than 1/n
return m3;
}
