StatStandardDeviation(ReadOnlyDoubleMatrix, Boolean) Method

Returns the standard deviation of the specified data, eventually adjusted for bias.

Definition

Namespace: Novacta.Analytics
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.1.0+428f3840cfab98dda567bb0ed350b302533e273a

C#

public static double StandardDeviation(
	ReadOnlyDoubleMatrix data,
	bool adjustForBias
)

VB

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

C++

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

F#

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

Parameters

data ReadOnlyDoubleMatrix: The data.
adjustForBias Boolean: If set to true signals that the standard deviation is adjusted for bias.

Return Value

Double
The standard deviation of the specified data, eventually adjusted for bias.

Remarks

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

where

is the central moment of order .

If adjustForBias is set to false, then the standard deviation is estimated through the coefficient

LaTeX equation

where

is the sample central moment of order , is the data length and

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

LaTeX equation

Example

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

C#

using System;

namespace Novacta.Analytics.CodeExamples
{
    public class StandardDeviationExample1  
    {
        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);

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

            // Compute the data standard deviation.
            var stdDev = Stat.StandardDeviation(matrix, adjustForBias);

            Console.WriteLine();
            Console.WriteLine("Data standard deviation is:");
            Console.WriteLine(stdDev);

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

            Console.WriteLine();
            Console.WriteLine("Using read-only data. The standard deviation is:");
            Console.WriteLine(stdDevOfReadOnlyData);
        }
    }
}

// Executing method Main() produces the following output:
// 
// The data matrix:
// 1                2                
// 2                -3               
// 3                4                
// 
// 
// 
// Data standard deviation is:
// 2.217355782608345
// 
// Using read-only data. The standard deviation is:
// 2.217355782608345

Exceptions

ArgumentNullException	data is null.
ArgumentException	adjustForBias is true and the number of entries in data is less than 2.