532 lines
24 KiB
MQL5
532 lines
24 KiB
MQL5
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//+------------------------------------------------------------------+
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//| ChiSquare.mqh |
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//| Copyright 2000-2025, MetaQuotes Ltd. |
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//| https://www.mql5.com |
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//+------------------------------------------------------------------+
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#include "Math.mqh"
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#include "Gamma.mqh"
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//+------------------------------------------------------------------+
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//| Chi-Square density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function |
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//| of the Chi-Square distribution with parameter nu. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| nu : Degrees of freedom |
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//| log_mode : Logarithm mode flag, if true it returns Log values |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The probability density evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityChiSquare(const double x,const double nu,const bool log_mode,int &error_code)
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{
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//--- check arguments
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if(!MathIsValidNumber(x) || !MathIsValidNumber(nu))
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{
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error_code=ERR_ARGUMENTS_NAN;
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return QNaN;
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}
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//--- nu must be positive integer
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if(nu<=0 || nu!=MathRound(nu))
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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error_code=ERR_OK;
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if(x<=0.0)
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return TailLog0(true,log_mode);
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//--- calculate using Gamma density
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double pdf=MathProbabilityDensityGamma(x,nu*0.5,2.0,error_code);
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if(log_mode==true)
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return MathLog(pdf);
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return pdf;
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}
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//+------------------------------------------------------------------+
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//| Chi-Square density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function |
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//| of the Chi-Square distribution with parameter nu. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| nu : Degrees of freedom |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The probability density evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityChiSquare(const double x,const double nu,int &error_code)
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{
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return MathProbabilityDensityChiSquare(x,nu,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Chi-Square density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of the |
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//| ChiSquare distribution with parameter nu for values in x[] array.|
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| nu : Degrees of freedom |
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//| log_mode : Logarithm mode flag, if true it returns Log values |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathProbabilityDensityChiSquare(const double &x[],const double nu,const bool log_mode,double &result[])
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{
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//--- check arguments
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if(!MathIsValidNumber(nu))
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return false;
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//--- nu must be positive integer
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if(nu<=0 || nu!=MathRound(nu))
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return false;
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int data_count=ArraySize(x);
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if(data_count==0)
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return false;
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int error_code=0;
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ArrayResize(result,data_count);
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for(int i=0; i<data_count; i++)
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{
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double x_arg=x[i];
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if(!MathIsValidNumber(x_arg))
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return false;
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if(x_arg<=0.0)
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result[i]=TailLog0(true,log_mode);
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else
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{
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//--- calculate using Gamma density
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double pdf=MathProbabilityDensityGamma(x_arg,nu*0.5,2.0,error_code);
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if(log_mode==true)
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result[i]=MathLog(pdf);
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else
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result[i]=pdf;
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}
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Chi-Square density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of the |
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//| ChiSquare distribution with parameter nu for values in x[] array.|
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| nu : Degrees of freedom |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathProbabilityDensityChiSquare(const double &x[],const double nu,double &result[])
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{
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return MathProbabilityDensityChiSquare(x,nu,false,result);
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}
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//+------------------------------------------------------------------+
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//| Chi-Square cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the cumulative distribution function of the |
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//| Chi-Square distribution with given nu, evaluated at x. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| nu : Degrees of freedom |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode, if true it calculates Log values |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of Chi-Square cumulative distribution function with |
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//| parameter nu, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionChiSquare(const double x,const double nu,const bool tail,const bool log_mode,int &error_code)
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{
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//--- check x
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if(!MathIsValidNumber(x) || !MathIsValidNumber(nu))
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{
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error_code=ERR_ARGUMENTS_NAN;
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return QNaN;
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}
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//--- nu must be positive integer
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if(nu<=0 || nu!=MathRound(nu))
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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error_code=ERR_OK;
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if(x<=0.0)
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return TailLog0(true,log_mode);
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//---- calculate using Gamma distribution
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return MathCumulativeDistributionGamma(x,nu*0.5,2.0,tail,log_mode,error_code);
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}
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//+------------------------------------------------------------------+
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//| Chi-Square cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the cumulative distribution function of the |
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//| Chi-Square distribution with given nu, evaluated at x. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| nu : Degrees of freedom |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of Chi-Square cumulative distribution function with |
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//| parameter nu, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionChiSquare(const double x,const double nu,int &error_code)
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{
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return MathCumulativeDistributionChiSquare(x,nu,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Chi-Square cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the cumulative distribution function of |
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//| the Chi-Square distribution with parameter nu for values in x[]. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| nu : Degrees of freedom |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode, if true it calculates Log values |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathCumulativeDistributionChiSquare(const double &x[],const double nu,const bool tail,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(nu))
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return false;
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//--- nu must be positive integer
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if(nu<=0 || nu!=MathRound(nu))
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return false;
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int data_count=ArraySize(x);
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if(data_count==0)
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return false;
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int error_code=0;
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ArrayResize(result,data_count);
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for(int i=0; i<data_count; i++)
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{
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double x_arg=x[i];
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if(!MathIsValidNumber(x_arg))
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return false;
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if(x_arg<=0.0)
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result[i]=TailLog0(true,log_mode);
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else
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{
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double cdf=MathCumulativeDistributionGamma(x_arg,nu*0.5,2.0,true,false,error_code);
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result[i]=TailLogValue(cdf,tail,log_mode);
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}
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Chi-Square cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the cumulative distribution function of |
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//| the Chi-Square distribution with parameter nu for values in x[]. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| nu : Degrees of freedom |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathCumulativeDistributionChiSquare(const double &x[],const double nu,double &result[])
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{
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return MathCumulativeDistributionChiSquare(x,nu,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Chi-Square distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the inverse cumulative distribution |
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//| function of the Chi-Square distribution with parameter nu |
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//| for the desired probability. |
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//| |
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//| Arguments: |
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//| probability : The desired probability |
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//| nu : Degrees of freedom |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode,if true it calculates for Log values|
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of the inverse cumulative distribution function |
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//| of the Chi-Square distribution with parameter nu. |
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//+------------------------------------------------------------------+
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double MathQuantileChiSquare(const double probability,const double nu,const bool tail,const bool log_mode,int &error_code)
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{
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//--- check NaN
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if(!MathIsValidNumber(nu))
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{
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error_code=ERR_ARGUMENTS_NAN;
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return QNaN;
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}
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//--- nu must be positive
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if(nu<=0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- nu must be integer
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if(nu!=MathRound(nu))
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- calculate real probability
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double prob=TailLogProbability(probability,tail,log_mode);
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//--- check probability range
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if(prob<0.0 || prob>1.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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error_code=ERR_OK;
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if(prob==0.0)
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return 0.0;
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if(prob==1.0)
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return QPOSINF;
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//---- calculate quantile using Gamma distribution
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return MathQuantileGamma(prob,nu*0.5,2.0,error_code);
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}
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//+------------------------------------------------------------------+
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//| Chi-Square distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the inverse cumulative distribution |
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//| function of the Chi-Square distribution with parameter nu |
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//| for the desired probability. |
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//| |
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//| Arguments: |
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//| probability : The desired probability |
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//| nu : Degrees of freedom |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of the inverse cumulative distribution function |
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//| of the Chi-Square distribution with parameter nu. |
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//+------------------------------------------------------------------+
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double MathQuantileChiSquare(const double probability,const double nu,int &error_code)
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{
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return MathQuantileChiSquare(probability,nu,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Chi-Square distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the inverse cumulative distribution |
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//| function of the Chi-Square distribution with parameter nu |
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//| for values from the probability[] array. |
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//| |
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//| Arguments: |
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//| probability : Array with probabilities |
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//| nu : Degrees of freedom |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode, if true it calculates Log values |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathQuantileChiSquare(const double &probability[],const double nu,const bool tail,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(nu))
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return false;
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//--- nu must be positive
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if(nu<=0)
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return false;
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//--- nu must be integer
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if(nu!=MathRound(nu))
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return false;
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int data_count=ArraySize(probability);
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if(data_count==0)
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return false;
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int error_code=0;
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ArrayResize(result,data_count);
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for(int i=0; i<data_count; i++)
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{
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//--- calculate real probability
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||
|
|
double prob=TailLogProbability(probability[i],tail,log_mode);
|
||
|
|
|
||
|
|
//--- check probability range
|
||
|
|
if(prob<0.0 || prob>1.0)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
if(prob==0.0)
|
||
|
|
result[i]=0.0;
|
||
|
|
else
|
||
|
|
if(prob==1.0)
|
||
|
|
result[i]=QPOSINF;
|
||
|
|
else
|
||
|
|
{
|
||
|
|
//--- calculate using Gamma distribution
|
||
|
|
result[i]=MathQuantileGamma(prob,nu*0.5,2.0,error_code);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Chi-Square distribution quantile function (inverse CDF) |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| The function calculates the inverse cumulative distribution |
|
||
|
|
//| function of the Chi-Square distribution with parameter nu |
|
||
|
|
//| for values from the probability[] array. |
|
||
|
|
//| |
|
||
|
|
//| Arguments: |
|
||
|
|
//| probability : Array with probabilities |
|
||
|
|
//| nu : Degrees of freedom |
|
||
|
|
//| result : Array with calculated values |
|
||
|
|
//| |
|
||
|
|
//| Return value: |
|
||
|
|
//| true if successful, otherwise false. |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
bool MathQuantileChiSquare(const double &probability[],const double nu,double &result[])
|
||
|
|
{
|
||
|
|
return MathQuantileChiSquare(probability,nu,true,false,result);
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Random variate from the Chi-Square distribution |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Computes the random variable from the Chi-Square distribution |
|
||
|
|
//| with parameter nu. |
|
||
|
|
//| |
|
||
|
|
//| Arguments: |
|
||
|
|
//| nu : Degrees of freedom |
|
||
|
|
//| error_code : Variable for error code |
|
||
|
|
//| |
|
||
|
|
//| Return value: |
|
||
|
|
//| The random value with Chi-Square distribution. |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
double MathRandomChiSquare(const double nu,int &error_code)
|
||
|
|
{
|
||
|
|
//--- NaN
|
||
|
|
if(!MathIsValidNumber(nu))
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_NAN;
|
||
|
|
return QNaN;
|
||
|
|
}
|
||
|
|
//--- nu must be integer
|
||
|
|
if(nu!=MathRound(nu))
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
||
|
|
return QNaN;
|
||
|
|
}
|
||
|
|
//--- nu must be positive
|
||
|
|
if(nu<=0)
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
||
|
|
return QNaN;
|
||
|
|
}
|
||
|
|
|
||
|
|
error_code=ERR_OK;
|
||
|
|
//--- return gamma(nu/2,2)
|
||
|
|
return MathRandomGamma(nu*0.5,2.0,error_code);
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Random variate from Chi-Square distribution |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Generates random variables from the Chi-Square distribution |
|
||
|
|
//| with parameter nu. |
|
||
|
|
//| |
|
||
|
|
//| Arguments: |
|
||
|
|
//| nu : Degrees of freedom |
|
||
|
|
//| data_count : Number of values needed |
|
||
|
|
//| result : Output array with random values |
|
||
|
|
//| |
|
||
|
|
//| Return value: |
|
||
|
|
//| true if successful, otherwise false. |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
bool MathRandomChiSquare(const double nu,const int data_count,double &result[])
|
||
|
|
{
|
||
|
|
//--- check NaN
|
||
|
|
if(!MathIsValidNumber(nu))
|
||
|
|
return false;
|
||
|
|
//--- nu must be integer
|
||
|
|
if(nu!=MathRound(nu))
|
||
|
|
return false;
|
||
|
|
//--- nu must be positive
|
||
|
|
if(nu<=0)
|
||
|
|
return false;
|
||
|
|
int error_code=0;
|
||
|
|
//--- prepare output array and calculate random values
|
||
|
|
ArrayResize(result,data_count);
|
||
|
|
for(int i=0; i<data_count; i++)
|
||
|
|
{
|
||
|
|
//--- generate Gamma random number
|
||
|
|
result[i]=MathRandomGamma(nu*0.5,2.0,error_code);
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Chi-Square distribution moments |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| The function calculates 4 first moments of Chi-Square |
|
||
|
|
//| distribution with parameter nu. |
|
||
|
|
//| |
|
||
|
|
//| Arguments: |
|
||
|
|
//| nu : Degrees of freedom |
|
||
|
|
//| mean : Variable for mean value (1st moment) |
|
||
|
|
//| variance : Variable for variance value (2nd moment) |
|
||
|
|
//| skewness : Variable for skewness value (3rd moment) |
|
||
|
|
//| kurtosis : Variable for kurtosis value (4th moment) |
|
||
|
|
//| error_code : Variable for error code |
|
||
|
|
//| |
|
||
|
|
//| Return value: |
|
||
|
|
//| true if moments calculated successfully, otherwise false. |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
bool MathMomentsChiSquare(const double nu,double &mean,double &variance,double &skewness,double &kurtosis,int &error_code)
|
||
|
|
{
|
||
|
|
//--- default values
|
||
|
|
mean =QNaN;
|
||
|
|
variance=QNaN;
|
||
|
|
skewness=QNaN;
|
||
|
|
kurtosis=QNaN;
|
||
|
|
//--- check NaN
|
||
|
|
if(!MathIsValidNumber(nu))
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_NAN;
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
//--- nu must be positive integer
|
||
|
|
if(nu<=0 || nu!=MathRound(nu))
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
error_code=ERR_OK;
|
||
|
|
//--- calculate moments
|
||
|
|
mean =nu;
|
||
|
|
variance=2*nu;
|
||
|
|
skewness=MathSqrt(8/nu);
|
||
|
|
kurtosis=12/nu;
|
||
|
|
//--- successful
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|