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Static Public Member Functions | List of all members
dsp.Statistics Class Reference

Provides functions for statistical analysis More...

Static Public Member Functions

static double Average (double[] A)
 Arithmetic mean More...
 
static double CMoment (double[] A, int order)
 Central Moment More...
 
static double CVariation (double[] A)
 Coefficient of variation (CV) More...
 
static double GeometricMean (double[] A)
 Geometric mean More...
 
static double HarmonicMean (double[] A)
 Harmonic mean More...
 
static double Kurtosis (double[] A)
 Kurtosis More...
 
static double MAD (double[] A)
 Mean Absolute Deviation (MAD) More...
 
static double Max (double[] A)
 Maximum More...
 
static double Max (double[] A, ref int index)
 Maximum More...
 
static double Median (double[] A)
 Median More...
 
static double Min (double[] A)
 Minimum More...
 
static double Min (double[] A, ref int index)
 Minimum More...
 
static double Moment (double[] A, int order)
 Sample Moment More...
 
static double RMS (double[] A)
 Root Mean Square More...
 
static double SDeviation (double[] A)
 Standard deviation More...
 
static double Skewness (double[] A)
 Skewness More...
 
static double Sum (double[] A)
 Sums all values of an array More...
 
static double SumOfSquares (double[] A)
 Sum of squares More...
 
static double Variance (double[] A)
 Variance More...
 

Detailed Description

Provides functions for statistical analysis

Member Function Documentation

◆ Average()

static double dsp.Statistics.Average ( double []  A)
static

Arithmetic mean

Parameters
Areal array
Returns
$\displaystyle \overline{x}=\frac{1}{N}\sum\limits_{i=1}^{N}x_i$

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double res = Statistics.Average(A);
Console.WriteLine(res);
5.5

◆ CMoment()

static double dsp.Statistics.CMoment ( double []  A,
int  order 
)
static

Central Moment

Parameters
Areal array
orderorder (positive)
Returns
$\displaystyle cm_k=\sum\limits_{i=1}^{N}(x_i-\overline{x})^k$

Example

double[] A = new double[6] { 1.1650, 0.6268, 0.0751, 0.3516, -0.6965, 1.6961 };
double res = Statistics.CMoment(A, 3);
Console.WriteLine(res);
-0.0281999891640001

◆ CVariation()

static double dsp.Statistics.CVariation ( double []  A)
static

Coefficient of variation (CV)

Parameters
Areal array
Returns
$\displaystyle CV=\frac{\sigma}{|\overline{x}|}100$

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double res = Statistics.CVariation(A);
Console.WriteLine(res);
56.5295700187201

◆ GeometricMean()

static double dsp.Statistics.GeometricMean ( double []  A)
static

Geometric mean

Parameters
Areal array
Returns
$\displaystyle G=\left[\prod\limits_{i=1}^{N}x_i\right]^{\displaystyle \frac{1}{N}}$

Example

double[] A = new double[4] { 1, 54, 2, 23 };
double res = Statistics.GeometricMean(A);
Console.WriteLine(res);
7.05972684864708

◆ HarmonicMean()

static double dsp.Statistics.HarmonicMean ( double []  A)
static

Harmonic mean

Parameters
Areal array
Returns
$\displaystyle H=\frac{N}{\sum\limits_{i=1}^{N}\displaystyle \frac{1}{x_i}}$

Example

double[] A = new double[4] { 1, 54, 2, 23 };
double res = Statistics.HarmonicMean(A);
Console.WriteLine(res);
2.56082474226804

◆ Kurtosis()

static double dsp.Statistics.Kurtosis ( double []  A)
static

Kurtosis

Parameters
Areal array
Returns
$\displaystyle k=\frac{\displaystyle \frac{1}{N}\sum\limits_{i=1}^{N}(x_i-\overline{x})^4}{\displaystyle\left[\frac{1}{N}\sum\limits_{i=1}^{N}(x_i-\overline{x})^2\right]^2}$

Example

double[] A = new double[5] { 1.1650, 0.6268, 0.0751, 0.3516, -0.6965 };
double res = Statistics.Kurtosis(A);
Console.WriteLine(res);
2.16588568029726

◆ MAD()

static double dsp.Statistics.MAD ( double []  A)
static

Mean Absolute Deviation (MAD)

Parameters
Areal array
Returns
$\displaystyle MAD=\frac{1}{N}\sum\limits_{i=1}^{N}|x_i-\overline{x}|$

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double res = Statistics.MAD(A);
Console.WriteLine(res);
2.5

◆ Max() [1/2]

static double dsp.Statistics.Max ( double []  A)
static

Maximum

Returns the maximum value found in an array

Parameters
Areal array

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double max = Statistics.Max(A);
Console.WriteLine(max);
9

◆ Max() [2/2]

static double dsp.Statistics.Max ( double []  A,
ref int  index 
)
static

Maximum

Returns the maximum value found in an array and the position index

Parameters
Areal array
indexposition index (return value)

Example

double[] A = new double[4] { 4, 2, 9, 7 };
int index = -1;
double max = Statistics.Max(A, ref index);
Console.WriteLine("Max:" + max + ", Index:" + index);
Max:9, Index:2

◆ Median()

static double dsp.Statistics.Median ( double []  A)
static

Median

The Median function sorts a set of real values in ascending order and returns the middle number. If there are two middle numbers an average value is calculated.

Parameters
Areal array

Example

double[] A = new double[4] { 1, 54, 2, 23 };
double res = Statistics.Median(A);
Console.WriteLine(res);
12.5

◆ Min() [1/2]

static double dsp.Statistics.Min ( double []  A)
static

Minimum

Returns the minimum value found in an array

Parameters
Areal array

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double min = Statistics.Min(A);
Console.WriteLine(min);
2

◆ Min() [2/2]

static double dsp.Statistics.Min ( double []  A,
ref int  index 
)
static

Minimum

Returns the minimum value found in an array and the position index

Parameters
Areal array
indexposition index (return value)

Example

double[] A = new double[4] { 4, 2, 9, 7 };
int index = -1;
double min = Statistics.Min(A, ref index);
Console.WriteLine("Min:" + min + ", Index:" + index);
Min:2, Index:1

◆ Moment()

static double dsp.Statistics.Moment ( double []  A,
int  order 
)
static

Sample Moment

Parameters
Areal array
orderorder (positive)
Returns
$\displaystyle m_k=\sum\limits_{i=1}^{N}x_i^k$

Example

double[] A = new double[6] { 1.1650, 0.6268, 0.0751, 0.3516, -0.6965, 1.6961 };
double res = Statistics.Moment(A, 3);
Console.WriteLine(res);
1.0687827153725

◆ RMS()

static double dsp.Statistics.RMS ( double []  A)
static

Root Mean Square

Parameters
Areal array
Returns
$\displaystyle {rms}=\sqrt{\frac{1}{N}\sum\limits_{i=1}^{N}x_i^2}$

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double res = Statistics.RMS(A);
Console.WriteLine(res);
6.12372435695795

◆ SDeviation()

static double dsp.Statistics.SDeviation ( double []  A)
static

Standard deviation

Parameters
Areal array
Returns
$\displaystyle \sigma=\sqrt{\frac{1}{N-1}\sum\limits_{i=1}^{N}(x_i-\overline{x})^2}$

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double res = Statistics.SDeviation(A);
Console.WriteLine(res);
3.1091263510296

◆ Skewness()

static double dsp.Statistics.Skewness ( double []  A)
static

Skewness

Parameters
Areal array
Returns
$\displaystyle s=\frac{\displaystyle \frac{1}{N}\sum\limits_{i=1}^{N}(x_i-\overline{x})^3}{\displaystyle\left[\sqrt{\frac{1}{N}\sum\limits_{i=1}^{N}(x_i-\overline{x})^2}\right]^3}$

Example

double[] A = new double[5] { 1.1650, 0.6268, 0.0751, 0.3516, -0.6965 };
double res = Statistics.Skewness(A);
Console.WriteLine(res);
-0.293223043366073

◆ Sum()

static double dsp.Statistics.Sum ( double []  A)
static

Sums all values of an array

Parameters
Areal array
Returns
$\displaystyle \sum\limits_{i=1}^{N}x_i$

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double res = Statistics.Sum(A);
Console.WriteLine(res);
22

◆ SumOfSquares()

static double dsp.Statistics.SumOfSquares ( double []  A)
static

Sum of squares

Parameters
Areal array
Returns
$\displaystyle \sum\limits_{i=1}^{N}x_i^2$

Example

double[] A = new double[4] { 1, 54, 2, 23 };
double res = Statistics.SumOfSquares(A);
Console.WriteLine(res);
3450

◆ Variance()

static double dsp.Statistics.Variance ( double []  A)
static

Variance

Parameters
Areal array
Returns
$\displaystyle \sigma^2=\frac{1}{N-1}\sum\limits_{i=1}^{N}(x_i-\overline{x})^2$

Example

double[] A = new double[4] { 4, 2, 9, 7 };
double res = Statistics.Variance(A);
Console.WriteLine(res);
9.66666666666667