521 lines
24 KiB
MQL5
521 lines
24 KiB
MQL5
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//+------------------------------------------------------------------+
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//| Exponential.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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//| Exponential density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function of |
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//| the Exponential distribution with parameter mu. |
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//| f(x,mu)=(1/mu)*exp(-x/mu) |
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//| Arguments: |
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//| x : Random variable |
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//| mu : Mean |
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//| log_mode : Logarithm mode flag, if true it returns 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 MathProbabilityDensityExponential(const double x,const double mu,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))
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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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//--- mu must be positive
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if(mu<=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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error_code=ERR_OK;
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//--- check x
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if(x<0.0)
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return TailLog0(true,log_mode);
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//--- calculate lambda;
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double lambda=1.0/mu;
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if(log_mode==true)
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return MathLog(lambda*MathExp(-x*lambda));
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//--- return density
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return lambda*MathExp(-x*lambda);
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}
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//+------------------------------------------------------------------+
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//| Exponential density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function of |
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//| the Exponential distribution with parameter mu. |
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//| f(x,mu)=(1/mu)*exp(-x/mu) |
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//| Arguments: |
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//| x : Random variable |
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//| mu : Mean |
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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 MathProbabilityDensityExponential(const double x,const double mu,int &error_code)
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{
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return MathProbabilityDensityExponential(x,mu,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Exponential density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of |
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//| the Exponential distribution with parameter mu for values in x. |
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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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//| 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 MathProbabilityDensityExponential(const double &x[],const double mu,const bool log_mode,double &result[])
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{
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//--- check parameters
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if(!MathIsValidNumber(mu))
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return false;
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//--- mu must be positive
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if(mu<=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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if(x_arg<0.0)
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result[i]=TailLog0(true,log_mode);
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else
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{
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//--- calculate lambda;
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double lambda=1.0/mu;
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if(log_mode==true)
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result[i]=MathLog(lambda*MathExp(-x_arg*lambda));
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else
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result[i]=lambda*MathExp(-x_arg*lambda);
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}
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Exponential density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of |
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//| the Exponential distribution with parameter mu for values in x. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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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 MathProbabilityDensityExponential(const double &x[],const double mu,double &result[])
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{
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return MathProbabilityDensityExponential(x,mu,false,result);
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}
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//+------------------------------------------------------------------+
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//| Exponential cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the cumulative distribution functin of the |
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//| Exponential distribution with parameter mu, evaluated at x. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| mu : Mean |
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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 Exponential cumulative distribution function |
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//| with parameter mu, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionExponential(const double x,const double mu,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))
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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 mu
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if(mu<=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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error_code=ERR_OK;
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//--- check x
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if(x<0.0)
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return TailLog0(tail,log_mode);
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//--- calculate cdf and take into account round-off errors for probability
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double result=MathMin(1.0-MathExp(-x/mu),1.0);
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return TailLogValue(result,tail,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Exponential cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the cumulative distribution function of the |
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//| Exponential distribution with parameter mu, evaluated at x. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| mu : Mean |
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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 Exponential cumulative distribution function |
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//| with parameter mu, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionExponential(const double x,const double mu,int &error_code)
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{
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return MathCumulativeDistributionExponential(x,mu,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Exponential 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 Exponential distribution with parameter mu for values in x[].|
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| a : Mean |
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//| b : Scale |
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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 MathCumulativeDistributionExponential(const double &x[],const double mu,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))
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return false;
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//--- check mu
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if(mu<=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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if(x_arg<0.0)
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result[i]=TailLog0(tail,log_mode);
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else
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{
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//--- calculate cdf and take into account round-off errors for probability
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double cdf=MathMin(1.0-MathExp(-x_arg/mu),1.0);
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result[i]=TailLogValue(cdf,tail,log_mode);
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}
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Exponential cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the cumulative distirbution function of |
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//| the Exponential distribution with parameter mu for values in x[].|
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| a : Mean |
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//| b : Scale |
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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 MathCumulativeDistributionExponential(const double &x[],const double mu,double &result[])
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{
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return MathCumulativeDistributionExponential(x,mu,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Exponential 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 Exponential distribution with parameter mu |
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//| 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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//| 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 inverse cumulative distribution function |
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//| of the Exponential distribution with parameter mu. |
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//+------------------------------------------------------------------+
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double MathQuantileExponential(const double probability,const double mu,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(mu))
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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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//--- mu must be positive
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if(mu<=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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error_code=ERR_OK;
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//--- check zero probability case
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if(prob==0.0)
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return 0.0;
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else
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if(prob==1.0)
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return QPOSINF;
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//--- return quantile
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return -mu*MathLog(1.0-prob);
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}
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//+------------------------------------------------------------------+
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//| Exponential 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 Exponential distribution with parameter mu |
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//| 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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//| 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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//| of the Exponential distribution with parameter mu. |
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//+------------------------------------------------------------------+
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double MathQuantileExponential(const double probability,const double mu,int &error_code)
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{
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return MathQuantileExponential(probability,mu,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Exponential distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the inverse cumulative distribution |
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//| function of the Exponential distribution with parameter mu |
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//| for values from the probability[] array. |
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//| |
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//| Arguments: |
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//| probability : Array with probabilities |
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//| mu : Mean |
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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 MathQuantileExponential(const double &probability[],const double mu,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))
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return false;
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//--- mu must be positive
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if(mu<=0.0)
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return false;
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int data_count=ArraySize(probability);
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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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//--- calculate real probability
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double prob=TailLogProbability(probability[i],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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return false;
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//--- check zero probability case
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if(prob==0.0)
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result[i]=0.0;
|
||
|
|
else
|
||
|
|
if(prob==1.0)
|
||
|
|
result[i]=QPOSINF;
|
||
|
|
else
|
||
|
|
result[i]=-mu*MathLog(1.0-prob);
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Exponential distribution quantile function (inverse CDF) |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| The function calculates the inverse cumulative distribution |
|
||
|
|
//| function of the Exponential distribution with parameter mu |
|
||
|
|
//| for values from the probability[] array. |
|
||
|
|
//| |
|
||
|
|
//| Arguments: |
|
||
|
|
//| probability : Array with probabilities |
|
||
|
|
//| mu : Mean |
|
||
|
|
//| result : Array with calculated values |
|
||
|
|
//| |
|
||
|
|
//| Return value: |
|
||
|
|
//| true if successful, otherwise false. |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
bool MathQuantileExponential(const double &probability[],const double mu,double &result[])
|
||
|
|
{
|
||
|
|
return MathQuantileExponential(probability,mu,true,false,result);
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Random variate from the Exponential distribution |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Compute the random variable from the Exponential distribution |
|
||
|
|
//| with parameter mu using simple inversion method. |
|
||
|
|
//| |
|
||
|
|
//| Arguments: |
|
||
|
|
//| mu : Mean |
|
||
|
|
//| error_code : Variable for error code |
|
||
|
|
//| |
|
||
|
|
//| Return value: |
|
||
|
|
//| The random value with Exponential distribution. |
|
||
|
|
//| |
|
||
|
|
//| Reference: |
|
||
|
|
//| Devroye L. "Non-uniform random variate generation",Springer,1986.|
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
double MathRandomExponential(const double mu,int &error_code)
|
||
|
|
{
|
||
|
|
//--- check mu
|
||
|
|
if(!MathIsValidNumber(mu))
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_NAN;
|
||
|
|
return QNaN;
|
||
|
|
}
|
||
|
|
//--- mu must be positive
|
||
|
|
if(mu<=0.0)
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
||
|
|
return QNaN;
|
||
|
|
}
|
||
|
|
|
||
|
|
error_code=ERR_OK;
|
||
|
|
//--- generate random number
|
||
|
|
double rnd=MathRandomNonZero();
|
||
|
|
//--- return variate using quantile
|
||
|
|
return -mu*MathLog(1.0-rnd);
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Random variate from the Exponential distribution |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Generates random variables from the Exponential distribution |
|
||
|
|
//| with parameter mu. |
|
||
|
|
//| |
|
||
|
|
//| Arguments: |
|
||
|
|
//| mu : Mean |
|
||
|
|
//| data_count : Number of values needed |
|
||
|
|
//| result : Output array with random values |
|
||
|
|
//| |
|
||
|
|
//| Return value: |
|
||
|
|
//| true if successful, otherwise false. |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
bool MathRandomExponential(const double mu,const int data_count,double &result[])
|
||
|
|
{
|
||
|
|
//--- check mu
|
||
|
|
if(!MathIsValidNumber(mu))
|
||
|
|
return false;
|
||
|
|
//--- mu must be positive
|
||
|
|
if(mu<=0.0)
|
||
|
|
return false;
|
||
|
|
//--- prepare output array and calculate random values
|
||
|
|
ArrayResize(result,data_count);
|
||
|
|
for(int i=0; i<data_count; i++)
|
||
|
|
{
|
||
|
|
//--- generate random number
|
||
|
|
double rnd=MathRandomNonZero();
|
||
|
|
result[i]=-mu*MathLog(1.0-rnd);
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| Exponential distribution moments |
|
||
|
|
//+------------------------------------------------------------------+
|
||
|
|
//| The function calculates 4 first moments of the Exponential |
|
||
|
|
//| distribution with parameter mu. |
|
||
|
|
//| |
|
||
|
|
//| Arguments: |
|
||
|
|
//| mu : Mean |
|
||
|
|
//| 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 MathMomentsExponential(const double mu,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))
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_NAN;
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
//--- mu must be positive
|
||
|
|
if(mu<=0.0)
|
||
|
|
{
|
||
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
error_code=ERR_OK;
|
||
|
|
//--- calculate moments
|
||
|
|
mean =mu;
|
||
|
|
variance=mu*mu;
|
||
|
|
skewness=2;
|
||
|
|
kurtosis=6;
|
||
|
|
//--- successful
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|