643 lines
28 KiB
MQL5
643 lines
28 KiB
MQL5
//+------------------------------------------------------------------+
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//| NegativeBinomial.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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#include "Gamma.mqh"
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#include "Poisson.mqh"
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//+------------------------------------------------------------------+
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//| Negative Binomial probability mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability mass function |
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//| of the Negative Binomial distribution with parameters r and p. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| r : Number of successes |
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//| p : Probability of success |
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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 mass evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityNegativeBinomial(const double x,const double r,const double p,const bool log_mode,int &error_code)
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{
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//--- check NaN
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if(!MathIsValidNumber(x) || !MathIsValidNumber(r) || !MathIsValidNumber(p))
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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 arguments
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if(r!=MathRound(r) || r<1.0 || p<0.0 || p>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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if(x<0.0)
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return TailLog0(true,log_mode);
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//--- calculate gamma factor for the density
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double coef=MathRound(MathExp(MathGammaLog(r+x)-MathGammaLog(x+1.0)-MathGammaLog(r)));
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//--- return density
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return TailLogValue(coef*MathPow(p,r)*MathPow(1.0-p,x),true,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Negative Binomial probability mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability mass function |
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//| of the Negative Binomial distribution with parameters r and p. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| r : Number of successes |
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//| p : Probability of success |
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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 mass evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityNegativeBinomial(const double x,const double r,const double p,int &error_code)
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{
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return MathProbabilityDensityNegativeBinomial(x,r,p,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Negative Binomial probability mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability mass function |
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//| of the Negative Binomial distribution with parameters r and p |
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//| for values from x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| r : Number of successes |
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//| p : Probability of success |
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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 MathProbabilityDensityNegativeBinomial(const double &x[],const double r,const double p,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(r) || !MathIsValidNumber(p))
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return false;
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//--- check arguments
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if(r!=MathRound(r) || r<1.0 || p<0.0 || p>1.0)
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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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double power_p_r=MathPow(p,r);
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double log_gamma_r=MathGammaLog(r);
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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 pdf
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double pdf=power_p_r*MathPow(1.0-p,x_arg)*MathRound(MathExp(MathGammaLog(r+x_arg)-MathGammaLog(x_arg+1.0)-log_gamma_r));
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result[i]=TailLogValue(pdf,true,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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//| Negative Binomial probability mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability mass function |
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//| of the Negative Binomial distribution with parameters r and p |
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//| for values from x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| r : Number of successes |
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//| p : Probability of success |
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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 MathProbabilityDensityNegativeBinomial(const double &x[],const double r,const double p,double &result[])
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{
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return MathProbabilityDensityNegativeBinomial(x,r,p,false,result);
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}
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//+------------------------------------------------------------------+
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//| Negative Binomial 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 Negative Binomial distribution with parameters r and p |
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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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//| r : Number of successes |
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//| p : Probability of success |
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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 Negative Binomial cumulative distribution |
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//| function with parameters r and p, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionNegativeBinomial(const double x,const double r,double p,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(x) || !MathIsValidNumber(r) || !MathIsValidNumber(p))
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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 arguments
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if(r!=MathRound(r) || r<1.0 || p<0.0 || p>1.0 || x<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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if(x<0.0)
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return TailLog0(tail,log_mode);
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int err_code=0;
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//--- calculate max term of the sum
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int max_j=(int)MathFloor(x);
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double p1=1.0-p;
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//--- initial factors
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double factor1=MathFactorial((int)r-1);
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double factor2=1.0;
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double factor_p=1.0;
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double factor_r=1.0/factor1;
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double power_p_r=MathPowInt(p,int(r))*factor_r;
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double cdf=0.0;
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for(int j=0; j<=max_j; j++)
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{
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if(j>0)
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{
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factor1*=(j+1);
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factor2*=j;
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factor_p*=p1;
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}
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double pdf=power_p_r*factor1*factor_p/factor2;
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cdf+=pdf;
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}
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//--- take into account round-off errors for probability
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return TailLogValue(MathMin(cdf,1.0),tail,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Negative Binomial 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 Negative Binomial distribution with parameters r and p |
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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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//| r : Number of successes |
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//| p : Probability of success |
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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 Negative Binomial cumulative distribution |
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//| function with parameters r and p, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionNegativeBinomial(const double x,const double r,double p,int error_code)
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{
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return MathCumulativeDistributionNegativeBinomial(x,r,p,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Negative Binomial cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the cumulative distribution function |
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//| of the Negative Binomial distribution with parameters r and p |
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//| for values from x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| r : Number of successes |
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//| p : Probability of success |
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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 MathCumulativeDistributionNegativeBinomial(const double &x[],const double r,double p,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(r) || !MathIsValidNumber(p))
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return false;
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//--- check arguments
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if(r!=MathRound(r) || r<1.0 || p<0.0 || p>1.0)
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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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//--- common factors
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double fact1=MathFactorial((int)r-1);
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double factor_r=1.0/fact1;
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double power_p_r=MathPowInt(p,int(r))*factor_r;
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double p1=1.0-p;
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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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int err_code=0;
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//--- calculate max term of the sum
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int max_j=(int)MathFloor(x_arg);
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//--- initial factors
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double factor1=fact1;
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double factor2=1.0;
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double factor_p=1.0;
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double cdf=0.0;
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for(int j=0; j<=max_j; j++)
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{
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if(j>0)
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{
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factor1*=(j+1);
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factor2*=j;
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factor_p*=p1;
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}
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double pdf=power_p_r*factor1*factor_p/factor2;
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cdf+=pdf;
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}
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//--- take into account round-off errors for probability
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result[i]=TailLogValue(MathMin(cdf,1.0),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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//| Negative Binomial cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the cumulative distribution function |
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//| of the Negative Binomial distribution with parameters r and p |
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//| for values from x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| r : Number of successes |
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//| p : Probability of success |
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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 MathCumulativeDistributionNegativeBinomial(const double &x[],const double r,double p,double &result[])
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{
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return MathCumulativeDistributionNegativeBinomial(x,r,p,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Negative Binomial 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 Negative Binomial distribution with parameters |
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//| r and p 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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//| r : Number of successes |
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//| p : Probability of success |
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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 Negative Binomial distribution with parameters r and p. |
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//+------------------------------------------------------------------+
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double MathQuantileNegativeBinomial(const double probability,const double r,const double p,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(probability) || !MathIsValidNumber(r) || !MathIsValidNumber(p))
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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 arguments
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if(r!=MathRound(r) || r<1.0 || p<0.0 || p>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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//--- 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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//--- check cases p=0 and p=1
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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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if(prob==0.0)
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return 0.0;
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int max_terms=1000;
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int err_code=0;
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//--- factors
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double fact1=MathFactorial((int)r-1);
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double factor_r=1.0/fact1;
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double power_p_r=MathPowInt(p,int(r))*factor_r;
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double p1=1.0-p;
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//--- initial factors
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double factor1=fact1;
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double factor2=1.0;
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double factor_p=1.0;
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double cdf=0.0;
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int j=0;
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while(cdf<prob && j<max_terms)
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{
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if(j>0)
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{
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factor1*=(j+1);
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factor2*=j;
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factor_p*=p1;
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}
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double pdf=power_p_r*factor1*factor_p/factor2;
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cdf+=pdf;
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j++;
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}
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//--- check convergence
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if(j<max_terms)
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{
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if(j==0)
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return 0;
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else
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return j-1;
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}
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else
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{
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error_code=ERR_NON_CONVERGENCE;
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return 0;
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}
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}
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//+------------------------------------------------------------------+
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//| Negative Binomial 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 Negative Binomial distribution with parameters |
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//| r and p 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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//| r : Number of successes |
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//| p : Probability of success |
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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 Negative Binomial distribution with parameters r and p. |
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//+------------------------------------------------------------------+
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double MathQuantileNegativeBinomial(const double probability,const double r,const double p,int &error_code)
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{
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return MathQuantileNegativeBinomial(probability,r,p,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Negative Binomial 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 Negative Binomial distribution with parameters |
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//| r and p for values form the probability[] array. |
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//| |
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//| Arguments: |
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//| probability : Array with probabilities |
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//| r : Number of successes |
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//| p : Probability of success |
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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 MathQuantileNegativeBinomial(const double &probability[],const double r,const double p,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(r) || !MathIsValidNumber(p))
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return false;
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//--- check arguments
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if(r!=MathRound(r) || r<1.0 || p<0.0 || p>1.0)
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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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//--- common factors
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double fact1=MathFactorial((int)r-1);
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double factor_r=1.0/fact1;
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double power_p_r=MathPowInt(p,int(r))*factor_r;
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double p1=1.0-p;
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int max_terms=500;
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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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if(prob==0.0)
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result[i]=0.0;
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else
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if(prob==1.0)
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result[i]=QPOSINF;
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else
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{
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double factor1=fact1;
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double factor2=1.0;
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double factor_p=1.0;
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double cdf=0.0;
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int j=0;
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while(cdf<prob && j<max_terms)
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{
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if(j>0)
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{
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factor1*=(j+1);
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factor2*=j;
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factor_p*=p1;
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}
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double pdf=power_p_r*factor1*factor_p/factor2;
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cdf+=pdf;
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j++;
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}
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if(j<max_terms)
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{
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if(j==0)
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result[i]=0;
|
|
else
|
|
result[i]=j-1;
|
|
}
|
|
else
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Negative Binomial distribution quantile function (inverse CDF) |
|
|
//+------------------------------------------------------------------+
|
|
//| The function calculates the inverse cumulative distribution |
|
|
//| function of the Negative Binomial distribution with parameters |
|
|
//| r and p for values from the probability[] array. |
|
|
//| |
|
|
//| Arguments: |
|
|
//| probability : Array with probabilities |
|
|
//| r : Number of successes |
|
|
//| p : Probability of success |
|
|
//| result : Array with calculated values |
|
|
//| |
|
|
//| Return value: |
|
|
//| true if successful, otherwise false. |
|
|
//+------------------------------------------------------------------+
|
|
bool MathQuantileNegativeBinomial(const double &probability[],const double r,const double p,double &result[])
|
|
{
|
|
return MathQuantileNegativeBinomial(probability,r,p,true,false,result);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Random variate from the Negative Binomial distribution |
|
|
//+------------------------------------------------------------------+
|
|
//| Computes the random variable from the Negative Binomial |
|
|
//| distribution with parameters r and p. |
|
|
//| |
|
|
//| Arguments: |
|
|
//| r : Number of successes |
|
|
//| p : Probability of success |
|
|
//| error_code : Variable for error code |
|
|
//| |
|
|
//| Return value: |
|
|
//| The random value with Negative Binomial distribution. |
|
|
//+------------------------------------------------------------------+
|
|
double MathRandomNegativeBinomial(const double r,const double p,int error_code)
|
|
{
|
|
//--- check NaN
|
|
if(!MathIsValidNumber(r) || !MathIsValidNumber(p))
|
|
{
|
|
error_code=ERR_ARGUMENTS_NAN;
|
|
return QNaN;
|
|
}
|
|
//--- check arguments
|
|
if(r<=0.0 || p<=0.0 || p>=1.0)
|
|
{
|
|
error_code=ERR_ARGUMENTS_NAN;
|
|
return QNaN;
|
|
}
|
|
double r_gamma=MathRandomGamma(r,(1-p)/p);
|
|
return MathRandomPoisson(r_gamma,error_code);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Random variate from the Negative Binomial distribution |
|
|
//+------------------------------------------------------------------+
|
|
//| Generates random variables from the Negative Binomial |
|
|
//| distribution with parameters r and p. |
|
|
//| |
|
|
//| Arguments: |
|
|
//| r : Number of successes |
|
|
//| p : Probability of success |
|
|
//| data_count : Number of values needed |
|
|
//| result : Output array with random values |
|
|
//| |
|
|
//| Return value: |
|
|
//| true if successful, otherwise false. |
|
|
//+------------------------------------------------------------------+
|
|
bool MathRandomNegativeBinomial(const double r,const double p,const int data_count,double &result[])
|
|
{
|
|
//--- check NaN
|
|
if(!MathIsValidNumber(r) || !MathIsValidNumber(p))
|
|
return false;
|
|
//--- check arguments
|
|
if(r<=0.0 || p<=0.0 || p>=1.0)
|
|
return false;
|
|
|
|
double p_coef=(1-p)/p;
|
|
int error_code=0;
|
|
//--- prepare output array and calculate random values
|
|
ArrayResize(result,data_count);
|
|
for(int i=0; i<data_count; i++)
|
|
{
|
|
double r_gamma=MathRandomGamma(r,p_coef);
|
|
result[i]=MathRandomPoisson(r_gamma,error_code);
|
|
}
|
|
return true;
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Negative Binomial distribution moments |
|
|
//+------------------------------------------------------------------+
|
|
//| The function calculates 4 first moments of Negative Binomial |
|
|
//| distribution with parameters r and p. |
|
|
//| |
|
|
//| Arguments: |
|
|
//| r : Number of successes |
|
|
//| p : Probability of success |
|
|
//| 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 MathMomentsNegativeBinomial(const double r,double p,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(r) || !MathIsValidNumber(p))
|
|
{
|
|
error_code=ERR_ARGUMENTS_NAN;
|
|
return false;
|
|
}
|
|
//--- check arguments
|
|
if(r!=MathRound(r) || r<1.0 || p<=0.0 || p>=1.0)
|
|
{
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
|
return false;
|
|
}
|
|
|
|
error_code=ERR_OK;
|
|
//--- calculate moments
|
|
mean =r*(1.0-p)/p;
|
|
variance=mean/p;
|
|
skewness=(2.0-p)/MathSqrt((r*(1.0-p)));
|
|
kurtosis=(p*p-6*p+6)/(r*(1.0-p));
|
|
//--- successful
|
|
return true;
|
|
}
|
|
//+------------------------------------------------------------------+
|