| //+------------------------------------------------------------------+
|
| //| Logistic.mqh |
|
| //| Copyright 2000-2025, MetaQuotes Ltd. |
|
| //| https://www.mql5.com |
|
| //+------------------------------------------------------------------+
|
| #include "Math.mqh"
|
|
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution density function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability density function of |
|
| //| the Logistic distribution with parameters mu and sigma. |
|
| //| f(x,mu,sigma)=exp[-(x-mu)/sigma]/(sigma*(exp[-(x-mu)/sigma])^2) |
|
| //| |
|
| //| Arguments: |
|
| //| x : Random variable |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| log_mode : Logarithm mode, if true it calculates Log values |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The probability density evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathProbabilityDensityLogistic(const double x,const double mu,const double sigma,const bool log_mode,int &error_code)
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(x) || !MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
| {
|
| error_code=ERR_ARGUMENTS_NAN;
|
| return QNaN;
|
| }
|
| //--- check sigma
|
| if(sigma<=0.0)
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
| //--- prepare argument
|
| double y=(x-mu)/sigma;
|
| //--- check result
|
| if(!MathIsValidNumber(y))
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
|
|
| error_code=ERR_OK;
|
|
|
| //--- calculate exponents
|
| double e=MathExp(-y);
|
| double e1=(1+e);
|
| double pdf=e/(sigma*(e1*e1));
|
| if(log_mode==true)
|
| return MathLog(pdf);
|
| //--- return logistic density
|
| return pdf;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution density function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability density function of |
|
| //| the Logistic distribution with parameters mu and sigma. |
|
| //| f(x,mu,sigma)=exp[-(x-mu)/sigma]/(sigma*(exp[-(x-mu)/sigma])^2) |
|
| //| |
|
| //| Arguments: |
|
| //| x : Random variable |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The probability density evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathProbabilityDensityLogistic(const double x,const double mu,const double sigma,int &error_code)
|
| {
|
| return MathProbabilityDensityLogistic(x,mu,sigma,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution density function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the probability density function of |
|
| //| the Logistic distribution with parameters mu and sigma |
|
| //| for values in x[] array. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| log_mode : Logarithm mode flag, if true it returns Log values |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathProbabilityDensityLogistic(const double &x[],const double mu,const double sigma,const bool log_mode,double &result[])
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
| return false;
|
| //--- check sigma
|
| if(sigma<=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<data_count; i++)
|
| {
|
| double x_arg=x[i];
|
|
|
| if(!MathIsValidNumber(x_arg))
|
| return false;
|
|
|
| //--- prepare argument
|
| double y=(x_arg-mu)/sigma;
|
| //--- check result
|
| if(!MathIsValidNumber(y))
|
| return false;
|
|
|
| //--- calculate exponents
|
| double e=MathExp(-y);
|
| double e1=(1+e);
|
| double pdf=e/(sigma*(e1*e1));
|
| if(log_mode==true)
|
| result[i]=MathLog(pdf);
|
| else
|
| result[i]=pdf;
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution density function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the probability density function of |
|
| //| the Logistic distribution with parameters mu and sigma for |
|
| //| values from x[] array. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathProbabilityDensityLogistic(const double &x[],const double mu,const double sigma,double &result[])
|
| {
|
| return MathProbabilityDensityLogistic(x,mu,sigma,false,result);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability that an observation |
|
| //| from the Logistic distribution with parameters mu and sigma |
|
| //| is less than or equal to x. |
|
| //| Arguments: |
|
| //| x : The desired quantile |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| 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 Logistic cumulative distribution function |
|
| //| F(x,mu,sigma)=1/(1+exp[-(x-mu)/sigma]) |
|
| //| with parameters mu and sigma, evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathCumulativeDistributionLogistic(const double x,const double mu,double sigma,const bool tail,const bool log_mode,int &error_code)
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(x) || !MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
| {
|
| error_code=ERR_ARGUMENTS_NAN;
|
| return QNaN;
|
| }
|
| //--- check sigma
|
| if(sigma<=0.0)
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
| //--- prepare argument
|
| double y=(x-mu)/sigma;
|
| //--- check result
|
| if(!MathIsValidNumber(y))
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
|
|
| error_code=ERR_OK;
|
| //--- calculate cdf and take into account round-off errors for probability
|
| double result=1.0/(1.0+MathExp(-y));
|
| return TailLogValue(MathMin(result,1.0),tail,log_mode);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability that an observation |
|
| //| from the Logistic distribution with parameters mu and sigma |
|
| //| is less than or equal to x. |
|
| //| Arguments: |
|
| //| x : The desired quantile |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The value of the Logistic cumulative distribution function |
|
| //| F(x,mu,sigma)=1/(1+exp[-(x-mu)/sigma]) |
|
| //| with parameters mu and sigma, evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathCumulativeDistributionLogistic(const double x,const double mu,double sigma,int &error_code)
|
| {
|
| return MathCumulativeDistributionLogistic(x,mu,sigma,true,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the cumulative distribution function of |
|
| //| the Logistic distribution with parameters mu and sigma for |
|
| //| values from the x[] array. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| 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 MathCumulativeDistributionLogistic(const double &x[],const double mu,const double sigma,const bool tail,const bool log_mode,double &result[])
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
| return false;
|
| //--- check sigma
|
| if(sigma<=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<data_count; i++)
|
| {
|
| double x_arg=x[i];
|
|
|
| if(!MathIsValidNumber(x_arg))
|
| return false;
|
|
|
| //--- prepare argument
|
| double y=(x_arg-mu)/sigma;
|
| //--- check result
|
| if(!MathIsValidNumber(y))
|
| return false;
|
| //--- calculate cdf and take into account round-off errors for probability
|
| double cdf=MathMin(1.0/(1.0+MathExp(-y)),1.0);
|
| result[i]=TailLogValue(cdf,tail,log_mode);
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the cumulative distribution function of |
|
| //| the Logistic distribution with parameters mu and sigma for |
|
| //| values from the x[] array. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathCumulativeDistributionLogistic(const double &x[],const double mu,const double sigma,double &result[])
|
| {
|
| return MathCumulativeDistributionLogistic(x,mu,sigma,true,false,result);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution quantile function (inverse CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the inverse cumulative distribution |
|
| //| function of the Logistic distribution with parameters mu |
|
| //| and sigma for the desired probability. |
|
| //| |
|
| //| Arguments: |
|
| //| probability : The desired probability |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| tail : Flag to calculate lower tail |
|
| //| log_mode : Logarithm mode,if true it calculates for Log values|
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The value of the inverse cumulative distribution function |
|
| //| Q(p,mu,sigma)= mu+sigma*log(p/(1-p)) |
|
| //| of the Logistic distribution with parameters mu and sigma. |
|
| //+------------------------------------------------------------------+
|
| double MathQuantileLogistic(const double probability,const double mu,const double sigma,const bool tail,const bool log_mode,int &error_code)
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(probability) || !MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
| {
|
| error_code=ERR_ARGUMENTS_NAN;
|
| return QNaN;
|
| }
|
| //--- check sigma
|
| if(sigma<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;
|
| }
|
|
|
| if(prob==0.0 || prob==1.0)
|
| {
|
| if(sigma==0.0)
|
| {
|
| error_code=ERR_OK;
|
| return mu;
|
| }
|
| else
|
| {
|
| error_code=ERR_RESULT_INFINITE;
|
| if(prob==0.0)
|
| return QNEGINF;
|
| else
|
| return QPOSINF;
|
| }
|
| }
|
|
|
| error_code=ERR_OK;
|
| //--- calculate quantile
|
| double q=MathLog(prob/(1.0-prob));
|
| //--- return rescaled/shifted quantile
|
| return mu+sigma*q;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution quantile function (inverse CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the inverse cumulative distribution |
|
| //| function of the Logistic distribution with parameters mu |
|
| //| and sigma for the desired probability. |
|
| //| |
|
| //| Arguments: |
|
| //| probability : The desired probability |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The value of the inverse cumulative distribution function |
|
| //| of the Logistic distribution with parameters mu and sigma. |
|
| //+------------------------------------------------------------------+
|
| double MathQuantileLogistic(const double probability,const double mu,const double sigma,int &error_code)
|
| {
|
| return MathQuantileLogistic(probability,mu,sigma,true,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution quantile function (inverse CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the inverse cumulative distribution |
|
| //| function of the Logistic distribution with parameters mu and |
|
| //| sigma for values from the probability[] array. |
|
| //| |
|
| //| Arguments: |
|
| //| probability : Array with probabilities |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| 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 MathQuantileLogistic(const double &probability[],const double mu,const double sigma,const bool tail,const bool log_mode,double &result[])
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
| return false;
|
| //--- check sigma
|
| if(sigma<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; i<data_count; i++)
|
| {
|
| //--- calculate real probability
|
| double prob=TailLogProbability(probability[i],tail,log_mode);
|
| //--- check probability range
|
| if(prob<0.0 || prob>1.0)
|
| return false;
|
|
|
| if(prob==0.0 || prob==1.0)
|
| {
|
| if(sigma==0.0)
|
| result[i]=mu;
|
| else
|
| {
|
| if(prob==0.0)
|
| result[i]=QNEGINF;
|
| else
|
| result[i]=QPOSINF;
|
| }
|
| }
|
| else
|
| {
|
| //--- calculate quantile
|
| double q=MathLog(prob/(1.0-prob));
|
| //--- rescaled/shifted quantile
|
| result[i]=mu+sigma*q;
|
| }
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution quantile function (inverse CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the inverse cumulative distribution |
|
| //| function of the Logistic distribution with parameters mu and |
|
| //| sigma for values from the probability[] array. |
|
| //| |
|
| //| Arguments: |
|
| //| probability : Array with probabilities |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathQuantileLogistic(const double &probability[],const double mu,const double sigma,double &result[])
|
| {
|
| return MathQuantileLogistic(probability,mu,sigma,true,false,result);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Random variate from the Logistic distribution |
|
| //+------------------------------------------------------------------+
|
| //| Compute the random variable from the Logistic distribution |
|
| //| with parameters mu and sigma. |
|
| //| |
|
| //| Arguments: |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The random value with Logistic distribution. |
|
| //+------------------------------------------------------------------+
|
| double MathRandomLogistic(const double mu,const double sigma,int &error_code)
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
| {
|
| error_code=ERR_ARGUMENTS_NAN;
|
| return QNaN;
|
| }
|
| //--- check sigma
|
| if(sigma<0.0)
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
|
|
| error_code=ERR_OK;
|
| //--- check sigma
|
| if(sigma==0.0)
|
| return mu;
|
| //--- generate random number
|
| double rnd=MathRandomNonZero();
|
| //--- return value
|
| return mu+sigma*MathLog(rnd/(1.0-rnd));
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Random variate from the Logistic distribution |
|
| //+------------------------------------------------------------------+
|
| //| Generates random variables from the Logistic distribution |
|
| //| with parameters mu and sigma. |
|
| //| |
|
| //| Arguments: |
|
| //| mu : Mean |
|
| //| sigma : Scale parameter |
|
| //| data_count : Number of values needed |
|
| //| result : Output array with random values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathRandomLogistic(const double mu,const double sigma,const int data_count,double &result[])
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
| return false;
|
| //--- check sigma
|
| if(sigma<0.0)
|
| return false;
|
|
|
| //--- prepare output array
|
| ArrayResize(result,data_count);
|
| //--- check sigma
|
| if(sigma==0.0)
|
| {
|
| for(int i=0; i<data_count; i++)
|
| result[i]=mu;
|
| return true;
|
| }
|
| //--- calculate random variables
|
| for(int i=0; i<data_count; i++)
|
| {
|
| //--- generate random number
|
| double rnd=MathRandomNonZero();
|
| //--- calculate logistic random number
|
| result[i]=mu+sigma*MathLog(rnd/(1.0-rnd));
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Logistic distribution moments |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates 4 first moments of the Logistic |
|
| //| distribution with parameters mu and sigma. |
|
| //| |
|
| //| Arguments: |
|
| //| mu : Mean parameter |
|
| //| sigma : Scale parameter |
|
| //| 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 MathMomentsLogistic(const double mu,const double sigma,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(mu) || !MathIsValidNumber(sigma))
|
| {
|
| error_code=ERR_ARGUMENTS_NAN;
|
| return false;
|
| }
|
| //--- check sigma
|
| if(sigma<=0.0)
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return false;
|
| }
|
| error_code=ERR_OK;
|
| //--- calculate moments
|
| mean =mu;
|
| variance=MathPow(M_PI*sigma,2)/3.0;
|
| skewness=0;
|
| kurtosis=(21.0/5.0)-3;
|
| //--- successful
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
