Statistics.mqh Functions – library MetaTrader 5

This library contains a set of basic statistical functions necessary for user data processing.

This library was first published in CodeBase at MQL4 – Statistica.mqh functions library. Some typos have been detected and corrected while transferring the functions to MQL5. The code has become more intuitively clear. Most functions have been written using the algorithms from S. Bulashov’s book “Statistics for traders”.

The library functions are as follows:

Function	Description
Mediana	Median calculation
Mediana50	Median calculation by 50% interquantile range
Average	Sample arithmetic mean calculation
Average50	Sample arithmetic mean calculation by 50% interquantile range
SweepCenter	Sweep center calculation
AverageOfEvaluations	Calculation of the average value of five upper evaluations
Variance	Sample variance calculation
ThirdCentralMoment	Third central moment calculation
FourthCentralMoment	Fourth central moment calculation
Asymmetry	Sample asymmetry calculation
Excess	Sample excess calculation
Excess2	Another method of the sample excess calculation
Gamma	Euler’s gamma function calculation, x>0.
GammaStirling	Euler’s gamma function value calculation, for x>33 (Stirling’s approximation)
VarianceOfSampleVariance	Calculating the variance of a sample variance
VarianceOfStandartDeviation	Calculating the variance of a standard deviation
VarianceOfAsymmetry	Sample asymmetry variance calculation
VarianceOfExcess	Sample excess variance calculation
VarianceOfAverage	Sample mean variance calculation
Log	Logarithm calculation
CensorCoeff	Censoring ratio calculation
HistogramLength	Calculating the optimal number of the histogram columns
Resize	Calculating the optimal number of the array elements for the histogram
Histogram	Creating the histogram to *.csv file
Cov	Sample covariation calculation
Corr	Sample correlation calculation
VarianceOfCorr	Sample correlation variance calculation
AutoCorr	Autocorrelation calculation
AutoCorrFunc	Autocorrelation function calculation
aCoeff	Calculating the a ratio in the linear regression equation (y=a*x+b)
bCoeff	Calculating the b ratio in the linear regression equation (y=a*x+b)
LineRegresErrors	Calculating the linear regression errors
eVariance	Calculating the linear regression errors variance
aVariance	Calculating the linear regression a parameter variance
bVariance	Calculating the linear regression b parameter variance
DeterminationCoeff	Determination ratio calculation
ArraySeparate	Splitting the arr[n][2] array in two arrays
ArrayUnion	Joining the two arrays into the array of arr[n][2] type
WriteArray	Writing the one-dimensional array to *.csv file
WriteArray2	Writing the two-dimensional array to *.csv file

The file can be included in the projects requiring random sample parameters processing, its parameters evaluation, histograms etc.

Let’s examine the call of some functions:

//+------------------------------------------------------------------+
//|                                                         test.mq5 |
//|                        Copyright 2012, MetaQuotes Software Corp. |
//|                                               |
//+------------------------------------------------------------------+
#property copyright "Copyright 2012, MetaQuotes Software Corp."
#property link      ""
#property version   "1.00"

#include <Statistics.mqh>
//+------------------------------------------------------------------+
//| Script program start function                                    |
//+------------------------------------------------------------------+
void OnStart()
  {
//--- specifying two values samples.
   double arrX[10]={3,4,5,2,3,4,5,6,4,7};
   double arrY[10]={7,4,1,2,1,6,9,2,1,5};
//--- calculating the mean
   double mx=Average(arrX);
   double my=Average(arrY);
//--- using the mean to calculate the variance
   double dx = Variance(arrX,mx);
   double dy = Variance(arrY,my);
//--- asymmetry value and excess
   double as=Asymmetry(arrX,mx,dx);
   double exc=Excess(arrX,mx,dx);
//--- covariation and correlation values
   double cov=Cov(arrX,arrY,mx,my);
   double corr=Corr(cov,dx,dy);
//--- showing results in the log file
   PrintFormat("mx=%.6e",mx);
   PrintFormat("my=%.6e",my);
   PrintFormat("dx=%.6e",dx);
   PrintFormat("dy=%.6e",dy);
   PrintFormat("As=%.6e",as);
   PrintFormat("exc=%.6e",exc);
   PrintFormat("cov=%.6e",cov);
   PrintFormat("corr=%.6e",corr);
  }

As you can see, most functions require the values (as input parameters) that can be calculated using other functions.

For example:

double dx = Variance(arrX,mx);

To calculate the variance, we have to calculate the mean at first. That gives a certain advantage regarding the calculations optimization. In case it is necessary to calculate the variance for several times, it will be better to find the mean once instead of doing it several times inside the function. That will save time.

This feature applies to most functions of the library.