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2012.04.05 12:31
Libraries

Statistics.mqh Functions - library for MetaTrader 5

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\MQL5\Include\
statistics.mqh (27.16 KB)view
\MQL5\Scripts\
test.mq5 (1.64 KB)view

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:

FunctionDescription
 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. |
//|                                              http://www.mql5.com |
//+------------------------------------------------------------------+
#property copyright "Copyright 2012, MetaQuotes Software Corp."
#property link      "http://www.mql5.com"
#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.

Translated from Russian by MetaQuotes Software Corp.
Original code: https://www.mql5.com/ru/code/866

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