StatVariance(ReadOnlyDoubleMatrix, Boolean) Method

Returns the variance 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 Variance(
	ReadOnlyDoubleMatrix data,
	bool adjustForBias
)

VB

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

C++

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

F#

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

Parameters

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

Return Value

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

Remarks

The variance 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 variance 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 estimator is corrected for bias and the variance is evaluated through the coefficient

LaTeX equation

Example

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

C#

using System;

namespace Novacta.Analytics.CodeExamples
{
    public class VarianceExample1  
    {
        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);

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

            // Compute the data variance.
            var variance = Stat.Variance(matrix, adjustForBias);

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

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

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

// Executing method Main() produces the following output:
// 
// The data matrix:
// 1                2                
// 2                -3               
// 3                4                
// 
// 
// 
// Data variance is:
// 4.916666666666667
// 
// Using read-only data. The variance is:
// 4.916666666666667

Exceptions

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