/// <summary>
/// Returns the sample cokurtosis 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="cokurtosisType"></param>
public static double Coskurtosis(double[] arrayA, double[] arrayB, CokurtosisType cokurtosisType)
{
double m4 = FourthCentralCrossMoment(arrayA, arrayB, cokurtosisType);
double sd1 = StandardDeviation(arrayA);
double sd2 = StandardDeviation(arrayB);
if (cokurtosisType == CokurtosisType.AAAB)
{
return(m4 / (sd1 * sd1 * sd1 * sd2));
}
if (cokurtosisType == CokurtosisType.AABB)
{
return(m4 / (sd1 * sd1 * sd2 * sd2));
}
return(m4 / (sd1 * sd2 * sd2 * sd2));
}
/// <summary>
/// Returns the sample fourth 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="cokurtosisType"></param>
private static double FourthCentralCrossMoment(double[] arrayA, double[] arrayB, CokurtosisType cokurtosisType)
{
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 m4 = 0;
if (cokurtosisType == CokurtosisType.AAAB)
{
for (int i = 0; i < n; i++)
{
m4 += (arrayA[i] - meanA) * (arrayA[i] - meanA) * (arrayA[i] - meanA) * (arrayB[i] - meanB);
}
}
else if (cokurtosisType == CokurtosisType.AABB)
{
for (int i = 0; i < n; i++)
{
m4 += (arrayA[i] - meanA) * (arrayA[i] - meanA) * (arrayB[i] - meanB) * (arrayB[i] - meanB);
}
}
else
{
for (int i = 0; i < n; i++)
{
m4 += (arrayA[i] - meanA) * (arrayB[i] - meanB) * (arrayB[i] - meanB) * (arrayB[i] - meanB);
}
}
m4 *= n * (n - 1) / ((n - 1.0) * (n - 2.0) * (n - 3.0)); //because this is the sample coskew multiply by n(n+1)/(n-1)(n-2)(n-3) rather than 1/n
return(m4);
}
/// <summary>
/// Returns the sample fourth 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="cokurtosisType"></param>
private static double FourthCentralCrossMoment(double[] arrayA, double[] arrayB, CokurtosisType cokurtosisType)
{
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 m4 = 0;
if (cokurtosisType == CokurtosisType.AAAB)
{
for (int i = 0; i < n; i++)
m4 += (arrayA[i] - meanA) * (arrayA[i] - meanA) * (arrayA[i] - meanA) * (arrayB[i] - meanB);
}
else if (cokurtosisType == CokurtosisType.AABB)
{
for (int i = 0; i < n; i++)
m4 += (arrayA[i] - meanA)*(arrayA[i] - meanA)*(arrayB[i] - meanB)*(arrayB[i] - meanB);
}
else
{
for (int i = 0; i < n; i++)
m4 += (arrayA[i] - meanA) * (arrayB[i] - meanB) * (arrayB[i] - meanB) * (arrayB[i] - meanB);
}
m4 *= n * (n - 1) / ((n - 1.0) * (n - 2.0) * (n - 3.0)); //because this is the sample coskew multiply by n(n+1)/(n-1)(n-2)(n-3) rather than 1/n
return m4;
}
/// <summary>
/// Returns the sample cokurtosis 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="cokurtosisType"></param>
public static double Coskurtosis(double[] arrayA, double[] arrayB, CokurtosisType cokurtosisType)
{
double m4 = FourthCentralCrossMoment(arrayA, arrayB, cokurtosisType);
double sd1 = StandardDeviation(arrayA);
double sd2 = StandardDeviation(arrayB);
if (cokurtosisType == CokurtosisType.AAAB)
return m4 / (sd1 * sd1 * sd1 * sd2);
if(cokurtosisType == CokurtosisType.AABB)
return m4 / (sd1 * sd1 * sd2 * sd2);
return m4 / (sd1 * sd2 * sd2 * sd2);
}
