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.