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mql5/Include/Math/Stat/Logistic.mqh

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2025-08-05 01:57:33 -04:00
//+------------------------------------------------------------------+
//| 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;
}
//+------------------------------------------------------------------+
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