574 строки
26 КиБ
MQL5
574 строки
26 КиБ
MQL5
 | //+------------------------------------------------------------------+
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//| Weibull.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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//| Weibull probability density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function |
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//| of the Weibull distribution with parameters a and b. |
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//| f(x,a,b)=[(a/b)*(x/b)^(a-1)]*exp(-(x/b)^a) |
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//| Arguments: |
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//| x : Random variable |
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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 MathProbabilityDensityWeibull(const double x,const double a,const double b,const bool log_mode,int &error_code)
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{
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//--- f(-infinity)=f(infinity)=0
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if(x==QPOSINF || x==QNEGINF)
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{
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error_code=ERR_OK;
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return TailLog0(true,log_mode);
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}
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//--- check parameters
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if(!MathIsValidNumber(x) || !MathIsValidNumber(a) || !MathIsValidNumber(b))
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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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//--- a and b must be positive
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if(a<=0 || b<=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)
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return TailLog0(true,log_mode);
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//--- calculate factor
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double pwr=MathPow(x/b,a-1);
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double pdf=(a/b)*pwr*MathExp(-(x/b)*pwr);
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if(log_mode==true)
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return MathLog(pdf);
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//--- return density
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return pdf;
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}
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//+------------------------------------------------------------------+
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//| Weibull probability density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function |
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//| of the Weibull distribution with parameters a and b. |
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//| f(x,a,b)=[(a/b)*(x/b)^(a-1)]*exp(-(x/b)^a) |
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//| Arguments: |
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//| x : Random variable |
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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 MathProbabilityDensityWeibull(const double x,const double a,const double b,int &error_code)
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{
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return MathProbabilityDensityWeibull(x,a,b,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Weibull probability density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of the |
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//| Weibull distribution with parameters a and b 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 : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 MathProbabilityDensityWeibull(const double &x[],const double a,const double b,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
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return false;
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//--- a and b must be positive
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if(a<=0 || b<=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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//--- f(-infinity)=f(infinity)=0
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if(x_arg==QPOSINF || x_arg==QNEGINF)
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result[i]=TailLog0(true,log_mode);
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else
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if(x_arg<=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 factor
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double pwr=MathPow(x_arg/b,a-1);
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double pdf=(a/b)*pwr*MathExp(-(x_arg/b)*pwr);
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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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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Weibull probability density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of the |
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//| Weibull distribution with parameters a and b 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 : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 MathProbabilityDensityWeibull(const double &x[],const double a,const double b,double &result[])
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{
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return MathProbabilityDensityWeibull(x,a,b,false,result);
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}
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//+------------------------------------------------------------------+
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//| Weibull 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 Weibull distribution with parameters a and b |
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//| is less than or equal to x. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 Weibull cumulative distribution function |
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//| F(a,b)=1-exp(-(x/b)^a) |
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//| with parameters a and b, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionWeibull(const double x,const double a,const double b,const bool tail,const bool log_mode,int &error_code)
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{
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//--- f(-infinity)=0
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if(x==QNEGINF)
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{
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error_code=ERR_OK;
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return TailLog0(tail,log_mode);
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}
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//--- f(+infinity)=1
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if(x==QPOSINF)
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{
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error_code=ERR_OK;
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return TailLog1(tail,log_mode);
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}
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//--- check parameters
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if(!MathIsValidNumber(x) || !MathIsValidNumber(a) || !MathIsValidNumber(b))
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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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//--- a and b must be positive
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if(a<=0 || b<=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)
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return TailLog0(tail,log_mode);
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//--- calculate probability and take into account round-off errors
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double cdf=MathMin(1.0-MathExp(-MathPow(x/b,a)),1.0);
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return TailLogValue(cdf,tail,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Weibull 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 Weibull distribution with parameters a and b |
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//| is less than or equal to x. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 Weibull cumulative distribution function |
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//| F(a,b)=1-exp(-(x/b)^a) |
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//| with parameters a and b, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionWeibull(const double x,const double a,const double b,int &error_code)
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{
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return MathCumulativeDistributionWeibull(x,a,b,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Weibull 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 Weibull distribution with parameters a and b 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 : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 MathCumulativeDistributionWeibull(const double &x[],const double a,const double b,const bool tail,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
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return false;
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//--- a and b must be positive
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if(a<=0 || b<=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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//--- f(-infinity)=0, f(+infinity)=1
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if(x_arg==QNEGINF)
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result[i]=TailLog0(tail,log_mode);
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else
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//--- f(+infinity)=1
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if(x_arg==QPOSINF)
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result[i]=TailLog1(tail,log_mode);
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else
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//--- check x
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if(x_arg<=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 probability and take into account round-off errors
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double cdf=MathMin(1.0-MathExp(-MathPow(x_arg/b,a)),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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//| Weibull 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 Weibull distribution with parameters a and b 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 : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 MathCumulativeDistributionWeibull(const double &x[],const double a,const double b,double &result[])
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{
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return MathCumulativeDistributionWeibull(x,a,b,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Weibull 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 Weibull distribution |
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//| Q(p,a,b)=b*((-ln(1-p)))^(1/a) |
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//| with parameters a and b 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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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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//| tail : Flag to calculate for 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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//| of the Weibull distribution with parameters a and b. |
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//+------------------------------------------------------------------+
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double MathQuantileWeibull(const double probability,const double a,const double b,const bool tail,const bool log_mode,int &error_code)
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{
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//--- check NaN
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if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
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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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//--- a and b must be positive
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if(a<=0 || b<=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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//--- f(1)=+infinity
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if(prob==1.0)
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{
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error_code=ERR_RESULT_INFINITE;
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return QPOSINF;
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}
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error_code=ERR_OK;
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//--- f(0)=0
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if(prob==0.0)
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return 0.0;
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//--- return quantile
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return b*MathPow(-MathLog(1.0-prob),1.0/a);
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}
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//+------------------------------------------------------------------+
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//| Weibull 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 Weibull distribution |
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//| Q(p,a,b)=b*((-ln(1-p)))^(1/a) |
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//| with parameters a and b 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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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 Weibull distribution with parameters a and b. |
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//+------------------------------------------------------------------+
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double MathQuantileWeibull(const double probability,const double a,const double b,int &error_code)
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{
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return MathQuantileWeibull(probability,a,b,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Weibull 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 Weibull distribution with parameters a and b |
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//| for the probability values from array. |
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//| |
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//| Arguments: |
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//| probability : Array with probabilities |
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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 MathQuantileWeibull(const double &probability[],const double a,const double b,const bool tail,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
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return false;
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//--- a and b must be positive
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if(a<=0 || b<=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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//--- f(1)=+infinity
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if(prob==1.0)
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result[i]=QPOSINF;
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//--- f(0)=0
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if(prob==0.0)
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result[i]=0.0;
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else
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//--- calc quantile
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result[i]=b*MathPow(-MathLog(1.0-prob),1.0/a);
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Weibull 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 Weibull distribution with parameters a and b |
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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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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 MathQuantileWeibull(const double &probability[],const double a,const double b,double &result[])
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{
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return MathQuantileWeibull(probability,a,b,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Random variate from the Weibull distribution |
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//+------------------------------------------------------------------+
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//| Computes the random variable from the Weibull distribution |
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//| with shape a and scale b. |
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//| |
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//| Arguments: |
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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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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 random value with Weibull distribution. |
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//+------------------------------------------------------------------+
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double MathRandomWeibull(const double a,const double b,int &error_code)
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{
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//--- check NaN
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if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
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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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//--- a and b must be positive
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if(a<=0 || b<=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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//--- generate random number
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double rnd=MathRandomNonZero();
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return b*MathPow(-MathLog(rnd),1.0/a);
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}
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//+------------------------------------------------------------------+
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//| Random variate from the Weibull distribution |
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//+------------------------------------------------------------------+
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//| Generates random variables from the Weibull distribution with |
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//| parameters a and b. |
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//| |
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//| Arguments: |
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//| a : Shape parameter of the distribution (a>0) |
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//| b : Scale parameter of the distribution (b>0) |
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//| data_count : Number of values needed |
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//| result : Output array with random 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 MathRandomWeibull(const double a,const double b,const int data_count,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
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return false;
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//--- a and b must be positive
| |||
if(a<=0 || b<=0)
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return false;
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//--- prepare output array and calculate random values
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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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//--- generate random number
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double rnd=MathRandomNonZero();
| |||
result[i]=b*MathPow(-MathLog(rnd),1.0/a);
| |||
}
| |||
return true;
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Weibull distribution moments |
| |||
//+------------------------------------------------------------------+
| |||
//| The function calculates 4 first moments of the Weibull |
| |||
//| distribution with parameters a and b. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| a : Shape parameter of the distribution (a>0) |
| |||
//| b : Scale parameter of the distribution (b>0) |
| |||
//| 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 MathMomentsWeibull(const double a,const double b,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(a) || !MathIsValidNumber(b))
| |||
{
| |||
error_code=ERR_ARGUMENTS_NAN;
| |||
return false;
| |||
}
| |||
//--- a and b must be positive
| |||
if(a<=0 || b<=0)
| |||
{
| |||
error_code=ERR_ARGUMENTS_INVALID;
| |||
return false;
| |||
}
| |||
| |||
error_code=ERR_OK;
| |||
//--- Gamma function values
| |||
double g1 = MathGamma(1+1.0/a);
| |||
double g2 = MathGamma(1+2.0/a);
| |||
double g3 = MathGamma(1+3.0/a);
| |||
double g4 = MathGamma(1+4.0/a);
| |||
//--- calculate moments
| |||
mean =b*g1;
| |||
variance=b*b*g2-MathPow(g1,2);
| |||
skewness=(2*g1*g1*g1-3*g1*g2+g3)*MathPow(g2-g1*g1,-1.5);
| |||
kurtosis=(-6*MathPow(g1,4)+12*MathPow(g1,2)*g2-3*MathPow(g2,2)-4*g1*g3+g4)*MathPow(g2-g1*g1,-2);
| |||
//--- successful
| |||
return true;
| |||
}
| |||
//+------------------------------------------------------------------+
|