StatStandardDeviation(ReadOnlyDoubleMatrix, Boolean, DataOperation) Method

public static DoubleMatrix StandardDeviation(
	ReadOnlyDoubleMatrix data,
	bool adjustForBias,
	DataOperation dataOperation
)

Public Shared Function StandardDeviation ( 
	data As ReadOnlyDoubleMatrix,
	adjustForBias As Boolean,
	dataOperation As DataOperation
) As DoubleMatrix

public:
static DoubleMatrix^ StandardDeviation(
	ReadOnlyDoubleMatrix^ data, 
	bool adjustForBias, 
	DataOperation dataOperation
)

static member StandardDeviation : 
        data : ReadOnlyDoubleMatrix * 
        adjustForBias : bool * 
        dataOperation : DataOperation -> DoubleMatrix 

Parameters

data  ReadOnlyDoubleMatrix

The data.

adjustForBias  Boolean

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

dataOperation  DataOperation

A constant to specify if the standard deviation is to be computed for rows or columns.

Return Value

The standard deviation of a random variable can be defined as follows:



where



is the central moment of order .

By interpreting rows or columns of data as samples drawn from random variables, this method returns the standard deviation estimates of such variables. Let and be the data number of rows and columns, respectively, and define

Operating on rows

If dataOperation is OnRows, then the method returns a column vector whose length equals the number of rows of data. The i-th entry of such column returns the standard deviation of the i-th data row.

If adjustForBias is set to false, then the standard deviation of the i-th row is estimated through the coefficient



where



is the sample -th central moment of the i-th row.

Such estimator is biased. If adjustForBias is set to true, then the variance estimator is corrected for bias and the i-th standard deviation is evaluated through the coefficient

Operating on columns

If dataOperation is OnColumns, then the method returns a row vector whose length is the data number of columns. The j-th entry of the returned row exposes the standard deviation of the j-th data column.

If adjustForBias is set to false, then the standard deviation of the j-th column is estimated through the coefficient



where



is the sample -th central moment of the j-th column.

Such estimator is biased. If adjustForBias is set to true, then the variance estimator is corrected for bias and the j-th standard deviation is evaluated through the coefficient

In the following example, row and column standard deviation estimates in a data matrix are computed.

using System;

namespace Novacta.Analytics.CodeExamples
{
    public class StandardDeviationExample0  
    {
        public void Main()
        {
            // Create a matrix.
            var data = new double[20] {
                1, 2, -3,  6, -2,
                2, 2,  2,  0,  7,
               -3, 2,  3,  2,  9,
                5, 2,  7, -1, -4
            };
            var matrix = DoubleMatrix.Dense(4, 5, data, StorageOrder.RowMajor);
            Console.WriteLine("The data matrix:");
            Console.WriteLine(matrix);

            // StandardDeviation can be adjusted for bias.
            bool adjustForBias = true;

            // Compute the standard deviation on columns.
            var stdDevOnColumns = Stat.StandardDeviation(matrix, adjustForBias, DataOperation.OnColumns);

            Console.WriteLine();
            Console.WriteLine("StandardDeviation on columns:");
            Console.WriteLine(stdDevOnColumns);

            // StandardDeviation is overloaded to accept data as a read-only matrix:
            // compute the standard deviation on rows using a read-only wrapper of the data matrix.
            ReadOnlyDoubleMatrix readOnlyMatrix = matrix.AsReadOnly();
            var stdDevOnRows = Stat.StandardDeviation(readOnlyMatrix, adjustForBias, DataOperation.OnRows);

            Console.WriteLine();
            Console.WriteLine("StandardDeviation on rows:");
            Console.WriteLine(stdDevOnRows);
        }
    }
}

// Executing method Main() produces the following output:
// 
// The data matrix:
// 1                2                -3               6                -2               
// 2                2                2                0                7                
// -3               2                3                2                9                
// 5                2                7                -1               -4               
// 
// 
// 
// StandardDeviation on columns:
// 3.30403793       0                4.11298756       3.09569594       6.45497224       
// 
// 
// 
// StandardDeviation on rows:
// 3.56370594       
// 2.60768096       
// 4.27784993       
// 4.4384682        
// 
//

Reference

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