StatKurtosis(ReadOnlyDoubleMatrix, Boolean) Method

public static double Kurtosis(
	ReadOnlyDoubleMatrix data,
	bool adjustForBias
)

Public Shared Function Kurtosis ( 
	data As ReadOnlyDoubleMatrix,
	adjustForBias As Boolean
) As Double

public:
static double Kurtosis(
	ReadOnlyDoubleMatrix^ data, 
	bool adjustForBias
)

static member Kurtosis : 
        data : ReadOnlyDoubleMatrix * 
        adjustForBias : bool -> float 

Parameters

data  ReadOnlyDoubleMatrix

The data.

adjustForBias  Boolean

If set to true signals that the kurtosis is adjusted for bias.

Return Value

The kurtosis of a random variable can be defined as follows:



where and are the cumulants of order 2 and 4, respectively, and



is the central moment of order .

The parameter can be estimated through the coefficient



where



is the sample central moment of order , is the dataCount and



Note that is undefined if the standard deviation of data is zero.

The statistic is a biased estimator of . However, provided that is greater than 3, it can be corrected for bias and the kurtosis evaluated through the coefficient

If adjustForBias is set to false, this method returns if it is defined, otherwise NaN is returned.

If adjustForBias is set to true, then this methods operates as follows.

• If is less than 4, i.e. the cumulant estimators cannot be corrected for bias, then an exception is thrown.
• Differently, if is defined, then is returned, otherwise the return value is NaN.

In the following example, the kurtosis of a data matrix is computed.

using System;

namespace Novacta.Analytics.CodeExamples
{
    public class KurtosisExample1  
    {
        public void Main()
        {
            // Create a matrix.
            var data = new double[6] {
                1,  2,
                2, -3,
                3,  4,
            };
            var matrix = DoubleMatrix.Dense(3, 2, data, StorageOrder.RowMajor);
            Console.WriteLine("The data matrix:");
            Console.WriteLine(matrix);

            // Kurtosis can be adjusted for bias.
            bool adjustForBias = false;

            // Compute the data kurtosis.
            var kurtosis = Stat.Kurtosis(matrix, adjustForBias);

            Console.WriteLine();
            Console.WriteLine("Data kurtosis is:");
            Console.WriteLine(kurtosis);

            // Kurtosis is overloaded to accept data as a read-only matrix:
            // compute the kurtosis using a read-only wrapper of the data matrix.
            ReadOnlyDoubleMatrix readOnlyMatrix = matrix.AsReadOnly();
            var kurtosisOfReadOnlyData = Stat.Kurtosis(readOnlyMatrix, adjustForBias);

            Console.WriteLine();
            Console.WriteLine("Using read-only data. The kurtosis is:");
            Console.WriteLine(kurtosisOfReadOnlyData);
        }
    }
}

// Executing method Main() produces the following output:
// 
// The data matrix:
// 1                2                
// 2                -3               
// 3                4                
// 
// 
// 
// Data kurtosis is:
// 0.1327204826199364
// 
// Using read-only data. The kurtosis is:
// 0.1327204826199364

Reference

Other Resources