593 lines
27 KiB
MQL5
593 lines
27 KiB
MQL5
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//+------------------------------------------------------------------+
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//| Logistic.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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//+------------------------------------------------------------------+
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//| Logistic distribution density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function of |
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//| the Logistic distribution with parameters mu and sigma. |
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//| f(x,mu,sigma)=exp[-(x-mu)/sigma]/(sigma*(exp[-(x-mu)/sigma])^2) |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| mu : Mean |
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//| sigma : Scale parameter |
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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 probability density evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityLogistic(const double x,const double mu,const double sigma,const bool log_mode,int &error_code)
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{
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//--- check parameters
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if(!MathIsValidNumber(x) || !MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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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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//--- check sigma
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if(sigma<=0.0)
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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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//--- prepare argument
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double y=(x-mu)/sigma;
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//--- check result
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if(!MathIsValidNumber(y))
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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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//--- calculate exponents
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double e=MathExp(-y);
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double e1=(1+e);
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double pdf=e/(sigma*(e1*e1));
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if(log_mode==true)
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return MathLog(pdf);
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//--- return logistic density
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return pdf;
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}
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//+------------------------------------------------------------------+
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//| Logistic distribution density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function of |
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//| the Logistic distribution with parameters mu and sigma. |
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//| f(x,mu,sigma)=exp[-(x-mu)/sigma]/(sigma*(exp[-(x-mu)/sigma])^2) |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| mu : Mean |
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//| sigma : Scale parameter |
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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 MathProbabilityDensityLogistic(const double x,const double mu,const double sigma,int &error_code)
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{
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return MathProbabilityDensityLogistic(x,mu,sigma,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Logistic distribution density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of |
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//| the Logistic distribution with parameters mu and sigma |
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//| 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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//| mu : Mean |
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//| sigma : Scale parameter |
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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 MathProbabilityDensityLogistic(const double &x[],const double mu,const double sigma,const bool log_mode,double &result[])
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{
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//--- check parameters
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if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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return false;
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//--- check sigma
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if(sigma<=0.0)
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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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//--- prepare argument
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double y=(x_arg-mu)/sigma;
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//--- check result
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if(!MathIsValidNumber(y))
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return false;
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//--- calculate exponents
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double e=MathExp(-y);
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double e1=(1+e);
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double pdf=e/(sigma*(e1*e1));
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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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return true;
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}
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//+------------------------------------------------------------------+
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//| Logistic distribution density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of |
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//| the Logistic distribution with parameters mu and sigma for |
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//| values from x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| mu : Mean |
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//| sigma : Scale parameter |
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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 MathProbabilityDensityLogistic(const double &x[],const double mu,const double sigma,double &result[])
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{
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return MathProbabilityDensityLogistic(x,mu,sigma,false,result);
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}
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//+------------------------------------------------------------------+
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//| Logistic cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability that an observation |
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//| from the Logistic distribution with parameters mu and sigma |
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//| is less than or equal to x. |
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//| Arguments: |
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//| x : The desired quantile |
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//| mu : Mean |
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//| sigma : Scale parameter |
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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 the Logistic cumulative distribution function |
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//| F(x,mu,sigma)=1/(1+exp[-(x-mu)/sigma]) |
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//| with parameters mu and sigma, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionLogistic(const double x,const double mu,double sigma,const bool tail,const bool log_mode,int &error_code)
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{
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//--- check parameters
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if(!MathIsValidNumber(x) || !MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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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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//--- check sigma
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if(sigma<=0.0)
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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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//--- prepare argument
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double y=(x-mu)/sigma;
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//--- check result
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if(!MathIsValidNumber(y))
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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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//--- calculate cdf and take into account round-off errors for probability
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double result=1.0/(1.0+MathExp(-y));
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return TailLogValue(MathMin(result,1.0),tail,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Logistic cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability that an observation |
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//| from the Logistic distribution with parameters mu and sigma |
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//| is less than or equal to x. |
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//| Arguments: |
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//| x : The desired quantile |
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//| mu : Mean |
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//| sigma : Scale parameter |
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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 Logistic cumulative distribution function |
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//| F(x,mu,sigma)=1/(1+exp[-(x-mu)/sigma]) |
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//| with parameters mu and sigma, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionLogistic(const double x,const double mu,double sigma,int &error_code)
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{
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return MathCumulativeDistributionLogistic(x,mu,sigma,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Logistic 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 Logistic distribution with parameters mu and sigma for |
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//| values from the x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| mu : Mean |
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//| sigma : Scale parameter |
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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 MathCumulativeDistributionLogistic(const double &x[],const double mu,const double sigma,const bool tail,const bool log_mode,double &result[])
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{
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//--- check parameters
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if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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return false;
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//--- check sigma
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if(sigma<=0.0)
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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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//--- prepare argument
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double y=(x_arg-mu)/sigma;
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//--- check result
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if(!MathIsValidNumber(y))
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return false;
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//--- calculate cdf and take into account round-off errors for probability
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double cdf=MathMin(1.0/(1.0+MathExp(-y)),1.0);
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result[i]=TailLogValue(cdf,tail,log_mode);
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Logistic 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 Logistic distribution with parameters mu and sigma for |
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//| values from the x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| mu : Mean |
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//| sigma : Scale parameter |
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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 MathCumulativeDistributionLogistic(const double &x[],const double mu,const double sigma,double &result[])
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{
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return MathCumulativeDistributionLogistic(x,mu,sigma,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Logistic 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 Logistic distribution with parameters mu |
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//| and sigma 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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//| mu : Mean |
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//| sigma : Scale parameter |
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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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//| Q(p,mu,sigma)= mu+sigma*log(p/(1-p)) |
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//| of the Logistic distribution with parameters mu and sigma. |
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//+------------------------------------------------------------------+
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double MathQuantileLogistic(const double probability,const double mu,const double sigma,const bool tail,const bool log_mode,int &error_code)
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{
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//--- check parameters
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if(!MathIsValidNumber(probability) || !MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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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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//--- check sigma
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if(sigma<0.0)
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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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//--- 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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if(prob==0.0 || prob==1.0)
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{
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if(sigma==0.0)
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{
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error_code=ERR_OK;
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return mu;
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}
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else
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{
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error_code=ERR_RESULT_INFINITE;
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if(prob==0.0)
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return QNEGINF;
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else
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return QPOSINF;
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}
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}
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error_code=ERR_OK;
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//--- calculate quantile
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double q=MathLog(prob/(1.0-prob));
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//--- return rescaled/shifted quantile
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return mu+sigma*q;
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}
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//+------------------------------------------------------------------+
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//| Logistic 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 Logistic distribution with parameters mu |
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//| and sigma 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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//| mu : Mean |
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//| sigma : Scale parameter |
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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 |
|
||
|
|
//| 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;
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|