StatSkewness(ReadOnlyDoubleMatrix, Boolean) Method

public static double Skewness(
	ReadOnlyDoubleMatrix data,
	bool adjustForBias
)

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

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

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

Parameters

data  ReadOnlyDoubleMatrix

The data.

adjustForBias  Boolean

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

Return Value

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



where and are the cumulants of order 2 and 3, respectively, and



is the central moment of order .

Index 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 2, a correction for bias is defined and the kurtosis evaluated through the coefficient

If adjustForBias is set to false, then 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 3, i.e. the correction for bias is undefined, then an exception is thrown.
• Differently, if is defined, then is returned, otherwise NaN.

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

using System;

namespace Novacta.Analytics.CodeExamples
{
    public class SkewnessExample1  
    {
        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);

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

            // Compute the data skewness.
            var skewness = Stat.Skewness(matrix, adjustForBias);

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

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

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

// Executing method Main() produces the following output:
// 
// The data matrix:
// 1                2                
// 2                -3               
// 3                4                
// 
// 
// 
// Data skewness is:
// -1.1007155393126171
// 
// Using read-only data. The skewness is:
// -1.1007155393126171

Reference

Other Resources