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//+------------------------------------------------------------------+ //| F.mqh | //| Copyright 2000-2026, MetaQuotes Ltd. | //| www.mql5.com | //+------------------------------------------------------------------+ #include "Math.mqh" #include "Beta.mqh" #include "ChiSquare.mqh" //+------------------------------------------------------------------+ //| F-density function (PDF) | //+------------------------------------------------------------------+ //| The function returns the probability density function of the | //| F-distribution with parameters nu1 and nu2. | //| | //| Arguments: | //| x : Random variable | //| nu1 : Numerator degrees of freedom | //| nu2 : Denominator degrees of freedom | //| log_mode : Logarithm mode flag, if true it returns Log values | //| error_code : Variable for error code | //| | //| Return value: | //| The probability density evaluated at x. | //+------------------------------------------------------------------+ double MathProbabilityDensityF(const double x,const double nu1,const double nu2,const bool log_mode,int &error_code) { //--- check NaN if(!MathIsValidNumber(x) || !MathIsValidNumber(nu1) || !MathIsValidNumber(nu2)) { error_code=ERR_ARGUMENTS_NAN; return QNaN; } //--- check arguments if(nu1!=MathRound(nu1) || nu1!=MathRound(nu1) || nu1<1 || nu2<1) { error_code=ERR_ARGUMENTS_INVALID; return QNaN; } error_code=ERR_OK; //--- check x if(x<=0) return TailLog0(true,log_mode); //--- calculate F density double value=MathPow((nu1/nu2),nu1*0.5)*MathPow(x,(nu1-2)*0.5)/MathBeta(nu1*0.5,nu2*0.5); value=value*MathPow(1.0+(nu1/nu2)*x,-(nu1+nu2)*0.5); if(log_mode==true) return MathLog(value); //--- return F density return value; } //+------------------------------------------------------------------+ //| F-density function (PDF) | //+------------------------------------------------------------------+ //| The function returns the probability density function of the | //| F-distribution with parameters nu1 and nu2. | //| | //| Arguments: | //| x : Random variable | //| nu1 : Numerator degrees of freedom | //| nu2 : Denominator degrees of freedom | //| error_code : Variable for error code | //| | //| Return value: | //| The probability density evaluated at x. | //+------------------------------------------------------------------+ double MathProbabilityDensityF(const double x,const double nu1,const double nu2,int &error_code) { return MathProbabilityDensityF(x,nu1,nu2,false,error_code); } //+------------------------------------------------------------------+ //| F-density function (PDF) | //+------------------------------------------------------------------+ //| The function calculates the probability density function of the | //| F distribution with parameters nu1 and nu2 for values in x[]. | //| | //| Arguments: | //| x : Array with random variables | //| nu1 : Numerator degrees of freedom | //| nu2 : Denominator degrees of freedom | //| log_mode : Logarithm mode flag, if true it returns Log values | //| result : Array with calculated values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathProbabilityDensityF(const double &x[],const double nu1,const double nu2,const bool log_mode,double &result[]) { //--- check NaN if(!MathIsValidNumber(nu1) || !MathIsValidNumber(nu2)) return false; //--- check arguments if(nu1!=MathRound(nu1) || nu1!=MathRound(nu1) || nu1<1 || nu2<1) return false; int data_count=ArraySize(x); if(data_count==0) return false; int error_code=0; ArrayResize(result,data_count); for(int i=0; i1.0) { error_code=ERR_ARGUMENTS_INVALID; return QNaN; } //--- check case probability==1 if(prob==1.0) { error_code=ERR_RESULT_INFINITE; return QPOSINF; } error_code=ERR_OK; if(prob==0.0) return 0.0; //--- calculate quantile using Beta distribution double qBeta=MathQuantileBeta(1.0-prob,nu2*0.5,nu1*0.5,error_code); //--- return quantile; return (nu2/qBeta-nu2)/nu1; } //+------------------------------------------------------------------+ //| F-distribution quantile function (inverse CDF) | //+------------------------------------------------------------------+ //| The function returns the inverse cumulative distribution | //| function of F-distribution with parameters nu1 and nu2 | //| for the desired probability. | //| | //| Arguments: | //| probability : The desired probability | //| nu1 : Numerator degrees of freedom | //| nu2 : Denominator degrees of freedom | //| error_code : Variable for error code | //| | //| Return value: | //| The value of the inverse cumulative distribution function | //| of F-distribution with parameters nu1 and nu2. | //+------------------------------------------------------------------+ double MathQuantileF(const double probability,const double nu1,const double nu2,int &error_code) { return MathQuantileF(probability,nu1,nu2,true,false,error_code); } //+------------------------------------------------------------------+ //| F-distribution quantile function (inverse CDF) | //+------------------------------------------------------------------+ //| The function calculates the inverse cumulative distribution | //| function of the F distribution with parameters nu1 and nu2 | //| for values from the probability[] array. | //| | //| Arguments: | //| probability : Array with probabilities | //| nu1 : Numerator degrees of freedom | //| nu2 : Denominator degrees of freedom | //| tail : Flag to calculate lower tail | //| log_mode : Logarithm mode, if true it calculates Log values | //| result : Array with calculated values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathQuantileF(const double &probability[],const double nu1,const double nu2,const bool tail,const bool log_mode,double &result[]) { //--- check NaN if(!MathIsValidNumber(nu1) || !MathIsValidNumber(nu2)) return false; //--- check arguments if(nu1!=MathRound(nu1) || nu2!=MathRound(nu2) || nu1<=0 || nu2<=0) return false; int data_count=ArraySize(probability); if(data_count==0) return false; int error_code=0; ArrayResize(result,data_count); for(int i=0; i1.0) return false; //--- check case probability==1,0 if(prob==0.0) result[i]=0.0; else if(prob==1.0) result[i]=QPOSINF; else { //--- calculate quantile using Beta distribution double qBeta=MathQuantileBeta(1.0-prob,nu2*0.5,nu1*0.5,error_code); result[i]=(nu2/qBeta-nu2)/nu1; } } return true; } //+------------------------------------------------------------------+ //| F-distribution quantile function (inverse CDF) | //+------------------------------------------------------------------+ //| The function calculates the inverse cumulative distribution | //| function of the F distribution with parameters nu1 and nu2 | //| for values from probability[] array. | //| | //| Arguments: | //| probability : Array with probabilities | //| nu1 : Numerator degrees of freedom | //| nu2 : Denominator degrees of freedom | //| result : Array with calculated values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathQuantileF(const double &probability[],const double nu1,const double nu2,double &result[]) { return MathQuantileF(probability,nu1,nu2,true,false,result); } //+------------------------------------------------------------------+ //| Random variate from the F-distribution | //+------------------------------------------------------------------+ //| Compute the random variable from F-distribution | //| with parameters nu1 and nu2. | //| | //| Arguments: | //| nu1 : Numerator degrees of freedom | //| nu2 : Denominator degrees of freedom | //| error_code : Variable for error code | //| | //| Return value: | //| The random value with F-distribution. | //+------------------------------------------------------------------+ double MathRandomF(const double nu1,const double nu2,int &error_code) { //--- check NaN if(!MathIsValidNumber(nu1) || !MathIsValidNumber(nu2)) { error_code=ERR_ARGUMENTS_NAN; return QNaN; } //--- check arguments if(nu1!=MathRound(nu1) || nu2!=MathRound(nu2) || nu1<=0 || nu2<=0) { error_code=ERR_ARGUMENTS_INVALID; return QNaN; } error_code=ERR_OK; //--- random F=ChiSquare(nu1)*nu2/ChiSquare(nu2)*nu1; double xnum = MathRandomGamma(nu1*0.5,1.0,error_code)*nu2; double xden = MathRandomGamma(nu2*0.5,1.0,error_code)*nu1; //--- double value=0.0; if(xden!=0) value= xnum/xden; else { error_code=ERR_NON_CONVERGENCE; value=QNaN; } //--- return random F return value; } //+------------------------------------------------------------------+ //| Random variate from the F distribution | //+------------------------------------------------------------------+ //| Generates random variables from the F distribution with | //| parameters nu1 and nu2. | //| | //| Arguments: | //| data_count : Number of values needed | //| result : Output array with random values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathRandomF(const double nu1,const double nu2,const int data_count,double &result[]) { //--- check NaN if(!MathIsValidNumber(nu1) || !MathIsValidNumber(nu2)) return false; //--- check arguments if(nu1!=MathRound(nu1) || nu2!=MathRound(nu2) || nu1<=0 || nu2<=0) return false; //--- prepare output array and calculate random values ArrayResize(result,data_count); for(int i=0; i2) mean=nu2/(nu2-2); if(nu2>4) variance=2*nu2*nu2*(nu1+nu2-2)/(nu1*(nu2-2)*(nu2-2)*(nu2-4)); if(nu2>6) skewness=2*MathSqrt(2)*MathSqrt(nu2-4)*(2*nu1+nu2-2)/(MathSqrt(nu1*(nu1+nu2-2))*(nu2-6)); if(nu2>8) kurtosis=12*(nu1*(5*nu2-22)*(nu1+nu2-2)+(nu2-4)*(nu2-2)*(nu2-2))/(nu1*(nu2-8)*(nu2-6)*(nu1+nu2-2)); //--- successful return true; } //+------------------------------------------------------------------+