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//+------------------------------------------------------------------+ //| Cauchy.mqh | //| Copyright 2000-2026, MetaQuotes Ltd. | //| www.mql5.com | //+------------------------------------------------------------------+ #include "Math.mqh" //+------------------------------------------------------------------+ //| Cauchy density function (PDF) | //+------------------------------------------------------------------+ //| Computes the value of the Cauchy probability density function | //| with parameters a and b at the desired quantile x. | //| | //| f(x,a,b)= 1/(pi*b*(1.0+((x-a)/b)^2) | //| Arguments: | //| x : Random variable | //| a : Mean | //| b : Scale | //| 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 MathProbabilityDensityCauchy(const double x,const double a,const double b,const bool log_mode,int &error_code) { //--- check NaN if(!MathIsValidNumber(x) || !MathIsValidNumber(a) || !MathIsValidNumber(b)) { error_code=ERR_ARGUMENTS_NAN; return QNaN; } //--- check scale if(b<=0.0) { error_code=ERR_ARGUMENTS_INVALID; return QNaN; } //--- prepare argument double y=(x-a)/b; //--- check result if(!MathIsValidNumber(y)) { error_code=ERR_ARGUMENTS_INVALID; return QNaN; } error_code=ERR_OK; if(log_mode==true) return -MathLog(M_PI*b*(1.0+y*y)); //--- return Cauchy density return 1.0/(M_PI*b*(1.0+y*y)); } //+------------------------------------------------------------------+ //| Cauchy density function (PDF) | //+------------------------------------------------------------------+ //| Computes the value of the Cauchy probability density function | //| with parameters a and b at the desired quantile x. | //| | //| f(x,a,b)= 1/(pi*b*(1.0+((x-a)/b)^2) | //| Arguments: | //| x : Random variable | //| a : Mean | //| b : Scale | //| error_code : Variable for error code | //| | //| Return value: | //| The probability density evaluated at x. | //+------------------------------------------------------------------+ double MathProbabilityDensityCauchy(const double x,const double a,const double b,int &error_code) { return MathProbabilityDensityCauchy(x,a,b,false,error_code); } //+------------------------------------------------------------------+ //| Cauchy density function (PDF) | //+------------------------------------------------------------------+ //| The function calculates the probability density function of | //| Cauchy distribution with parameters a and b for values | //| from x[] array. | //| | //| Arguments: | //| x : Array with random variables | //| a : Mean | //| b : Scale | //| log_mode : Logarithm mode flag, if true it returns Log values | //| result : Array with calculated values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathProbabilityDensityCauchy(const double &x[],const double a,const double b,const bool log_mode,double &result[]) { //--- check NaN if(!MathIsValidNumber(a) || !MathIsValidNumber(b)) return false; //--- check scale if(b<=0.0) 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; i-1.0) cdf=MathMin(0.5+M_1_PI*MathArctan(y),1.0); else cdf=MathMin(M_1_PI*MathArctan(-1/y),1.0); return TailLogValue(cdf,tail,log_mode); } //+------------------------------------------------------------------+ //| Cauchy cumulative distribution function (CDF) | //+------------------------------------------------------------------+ //| The function returns the cumulative distribution function of | //| the Cauchy distribution with parameters a and b, evaluated at x. | //| | //| Arguments: | //| x : The desired quantile | //| a : Mean | //| b : Scale | //| error_code : Variable for error code | //| | //| The value of the Cauchy cumulative distribution function with | //| parameters a and b, evaluated at x. | //+------------------------------------------------------------------+ double MathCumulativeDistributionCauchy(const double x,const double a,const double b,int &error_code) { return MathCumulativeDistributionCauchy(x,a,b,true,false,error_code); } //+------------------------------------------------------------------+ //| Cauchy cumulative distribution function (CDF) | //+------------------------------------------------------------------+ //| The function calculates the cumulative distribution function of | //| the Cauchy distribution with parameters a and b for values from | //| x[] array. | //| | //| Arguments: | //| x : Array with random variables | //| a : Mean | //| b : Scale | //| tail : Flag to calculate lower tail | //| log_mode : Logarithm mode flag,if true it calculates Log values| //| error_code : Variable for error code | //| result : Array with calculated values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathCumulativeDistributionCauchy(const double &x[],const double a,const double b,const bool tail,const bool log_mode,double &result[]) { //--- check parameters if(!MathIsValidNumber(a) || !MathIsValidNumber(b)) return false; //--- check scale if(b<=0.0) 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; i-1.0) cdf=MathMin(0.5+M_1_PI*MathArctan(y),1.0); else cdf=MathMin(M_1_PI*MathArctan(-1/y),1.0); result[i]=TailLogValue(cdf,tail,log_mode); } return true; } //+------------------------------------------------------------------+ //| Cauchy cumulative distribution function (CDF) | //+------------------------------------------------------------------+ //| The function calculates the cumulative distribution function | //| of the Cauchy distribution with parameters a and b for values | //| from x[] array. | //| | //| Arguments: | //| x : Array with random variables | //| a : Mean | //| b : Scale | //| result : Array with calculated values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathCumulativeDistributionCauchy(const double &x[],const double a,const double b,double &result[]) { return MathCumulativeDistributionCauchy(x,a,b,true,false,result); } //+------------------------------------------------------------------+ //| Cauchy distribution quantile function (inverse CDF) | //+------------------------------------------------------------------+ //| The function returns the inverse cumulative distribution | //| function of the Cauchy distribution with parameters a and b | //| for the desired probability. | //| Q(p,a,b)=a+b*tan*(pi*(p-1/2)) | //| Arguments: | //| probability : The desired probability | //| a : Mean | //| b : Scale | //| tail : Flag to calculate lower tail | //| log_mode : Logarithm mode, if true it calculates Log values | //| error_code : Variable for error code | //| | //| Return value: | //| The value of the inverse cumulative distribution function | //| of the Cauchy distribution with parameters a and b. | //+------------------------------------------------------------------+ double MathQuantileCauchy(const double probability,const double a,const double b,const bool tail,const bool log_mode,int &error_code) { //--- check NaN if(!MathIsValidNumber(probability) || !MathIsValidNumber(a) || !MathIsValidNumber(b)) { error_code=ERR_ARGUMENTS_NAN; return QNaN; } //--- check scale if(b<=0.0) { error_code=ERR_ARGUMENTS_INVALID; return QNaN; } //--- calculate real probability double prob=TailLogProbability(probability,tail,log_mode); //--- check probability range if(prob<0.0 || prob>1.0) { error_code=ERR_ARGUMENTS_INVALID; return QNaN; } //--- f(1)= + infinity if(prob==1.0) { error_code=ERR_RESULT_INFINITE; return QPOSINF; } //--- f(0)= - infinity if(prob==0.0) { error_code=ERR_RESULT_INFINITE; return QNEGINF; } error_code=ERR_OK; //--- return quantile return a+b*MathTan(M_PI*(prob-0.5)); } //+------------------------------------------------------------------+ //| Cauchy distribution quantile function (inverse CDF) | //+------------------------------------------------------------------+ //| The function returns the inverse cumulative distribution | //| function of the Cauchy distribution with parameters a and b | //| for the desired probability. | //| | //| Arguments: | //| probability : The desired probability | //| a : Mean | //| b : Scale | //| error_code : Variable for error code | //| | //| Return value: | //| The value of the inverse cumulative distribution function | //| of the Cauchy distribution with parameters a and b. | //+------------------------------------------------------------------+ double MathQuantileCauchy(const double probability,const double a,const double b,int &error_code) { return MathQuantileCauchy(probability,a,b,true,false,error_code); } //+------------------------------------------------------------------+ //| Cauchy distribution quantile function (inverse CDF) | //+------------------------------------------------------------------+ //| The function returns the inverse cumulative distribution | //| function of the Cauchy distribution with parameters a and b | //| for the probability values from array. | //| | //| Arguments: | //| probability : Array with probabilities | //| a : Mean | //| b : Scale | //| result : Array with calculated values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathQuantileCauchy(const double &probability[],const double a,const double b,const bool tail,const bool log_mode,double &result[]) { //--- check NaN if(!MathIsValidNumber(a) || !MathIsValidNumber(b)) return false; //--- check scale if(b<=0.0) 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; //--- f(1)= + infinity if(prob==1.0) result[i]=QPOSINF; else //--- f(0)= - infinity if(prob==0.0) result[i]=QNEGINF; else result[i]=a+b*MathTan(M_PI*(prob-0.5)); } return true; } //+------------------------------------------------------------------+ //| Cauchy distribution quantile function (inverse CDF) | //+------------------------------------------------------------------+ bool MathQuantileCauchy(const double &probability[],const double a,const double b,double &result[]) { return MathQuantileCauchy(probability,a,b,true,false,result); } //+------------------------------------------------------------------+ //| Random variate from the Cauchy distribution | //+------------------------------------------------------------------+ //| Compute the random variable from the Cauchy distribution | //| with parameters a and b. | //| | //| Arguments: | //| a : Mean | //| b : Scale | //| error_code : Variable for error code | //| | //| Return value: | //| The random value with Cauchy distribution. | //+------------------------------------------------------------------+ double MathRandomCauchy(const double a,const double b,int &error_code) { //--- check parameters if(!MathIsValidNumber(a) || !MathIsValidNumber(b)) { error_code=ERR_ARGUMENTS_NAN; return QNaN; } //--- check scale if(b<0) { error_code=ERR_ARGUMENTS_INVALID; return QNaN; } error_code=ERR_OK; //--- check scale=0 if(b==0.0) return a; //--- generate random number double rnd=MathRandomNonZero(); //--- return result return a+b*MathTan(M_PI*(rnd-0.5)); } //+------------------------------------------------------------------+ //| Random variate from the Cauchy distribution | //+------------------------------------------------------------------+ //| Generates random variables from the Cauchy distribution with | //| parameters a and b. | //| | //| Arguments: | //| a : Mean | //| b : Scale | //| data_count : Number of values needed | //| result : Output array with random values | //| | //| Return value: | //| true if successful, otherwise false. | //+------------------------------------------------------------------+ bool MathRandomCauchy(const double a,const double b,const int data_count,double &result[]) { //--- check parameters if(!MathIsValidNumber(a) || !MathIsValidNumber(b)) return false; //--- check scale if(b<0) return false; //--- prepare output array ArrayResize(result,data_count); //--- check scale=0 if(b==0.0) { for(int i=0; i