754 lines
34 KiB
MQL5
754 lines
34 KiB
MQL5
//+------------------------------------------------------------------+
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//| Hypergeometric.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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//| Hypergeometric 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 Hypergeometric distribution with parameters m,n,k. |
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//| f(x,m,k,n)=C(k,x)*C(m-k,n-x)/C(m,n) |
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//| where binomial coefficient C(n,k)=n!/(k!*(n-k)! |
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//| |
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//| Arguments: |
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//| x : The desired number of objects |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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 function, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityHypergeometric(const double x,const double m,const double k,const double n,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(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
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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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//--- m,k,n must be integer
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if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n))
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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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//--- m,k,n must be positive
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if(m<0 || k<0 || n<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 ranges
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if(n>m || k>m)
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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 ranges
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if(x>n)
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return TailLog0(true,log_mode);
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if(x>k || m-k-n+x+1<=0)
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return TailLog0(true,log_mode);
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//--- calculate log binomial coefficients
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double log_pdf=MathBinomialCoefficientLog(k,x)+MathBinomialCoefficientLog(m-k,n-x)-MathBinomialCoefficientLog(m,n);
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if(log_mode==true)
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return log_pdf;
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//--- return hypergeometric density
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return MathExp(log_pdf);
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}
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//+------------------------------------------------------------------+
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//| Hypergeometric 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 Hypergeometric distribution with parameters m,n,k. |
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//| f(x,m,k,n)=C(k,x)*C(m-k,n-x)/C(m,n) |
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//| where binomial coefficient C(n,k)=n!/(k!*(n-k)! |
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//| |
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//| Arguments: |
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//| x : The desired number of objects |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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 function, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityHypergeometric(const double x,const double m,const double k,const double n,int &error_code)
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{
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return MathProbabilityDensityHypergeometric(x,m,k,n,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Hypergeometric probability mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability mass function of the |
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//| Hypergeometric distribution with parameter m,k,n 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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//| x : The desired number of objects |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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 MathProbabilityDensityHypergeometric(const double &x[],const double m,const double k,const double n,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
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return false;
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//--- m,k,n must be integer
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if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n))
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return false;
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//--- m,k,n must be positive
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if(m<0 || k<0 || n<0)
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return false;
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//--- check ranges
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if(n>m || k>m)
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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 m_k=m-k;
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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 || x_arg!=MathRound(x_arg))
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return false;
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if(x_arg>n)
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result[i]=TailLog0(true,log_mode);
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else
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//--- check ranges
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if(x_arg>k || m_k-n+x_arg+1<=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 log binomial coefficients
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double log_pdf=MathBinomialCoefficientLog(k,x_arg)+MathBinomialCoefficientLog(m_k,n-x_arg)-MathBinomialCoefficientLog(m,n);
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if(log_mode==true)
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result[i]=log_pdf;
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else
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result[i]=MathExp(log_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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//| Hypergeometric probability mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability mass function of the |
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//| Hypergeometric distribution with parameter m,k,n 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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//| x : The desired number of objects |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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 MathProbabilityDensityHypergeometric(const double &x[],const double m,const double k,const double n,double &result[])
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{
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return MathProbabilityDensityHypergeometric(x,m,k,n,false,result);
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}
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//+------------------------------------------------------------------+
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//| Hypergeometric 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 Hypergeometric distribution with parameters m,n,k |
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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 number of objects |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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 Hypergeometric cumulative distribution function |
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//| with parameters m,n,k, evaluated at x. |
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//+------------------------------------------------------------------+
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//| Based on algorithm by John Burkardt |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionHypergeometric(const double x,const double m,const double k,const double n,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(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
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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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//--- m,k,n,x must be integer
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if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n) || x!=MathRound(x))
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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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//--- m,k,n,x must be positive
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if(m<0 || k<0 || n<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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//--- check ranges
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if(n>m || k>m)
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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>=n || x>=k)
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return TailLog1(tail,log_mode);
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//--- calculate cdf
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double pdf = MathExp(MathBinomialCoefficientLog(m-k,n)-MathBinomialCoefficientLog(m,n));
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double cdf = pdf;
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double coef=m-k-n+1;
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for(int j=0; j<=x-1; j++)
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{
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pdf = pdf*(k-j)*(n-j)/((j+1)*(coef+j));
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cdf = cdf + pdf;
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}
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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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//| Hypergeometric 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 Hypergeometric distribution with parameters m,n,k |
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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 number of objects |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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 Hypergeometric cumulative distribution function |
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//| with parameters m,n,k, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionHypergeometric(const double x,const double m,const double k,const double n,int &error_code)
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{
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return MathCumulativeDistributionHypergeometric(x,m,k,n,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Hypergeometric 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 Hypergeometric distribution with parameters m,k,n for |
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//| the values in x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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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//| Based on algorithm by John Burkardt |
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//+------------------------------------------------------------------+
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bool MathCumulativeDistributionHypergeometric(const double &x[],const double m,const double k,const double n,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(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
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return false;
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//--- m,k,n,x must be integer
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if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n))
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return false;
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//--- m,k,n must be positive
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if(m<0 || k<0 || n<0)
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return false;
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//--- check ranges
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if(n>m || k>m)
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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 coef=m-k-n+1;
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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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//--- x must be positive and integer
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if(x_arg<0 || x_arg!=MathRound(x_arg))
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return false;
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//--- check ranges
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if(x_arg>=n || x_arg>=k)
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result[i]=TailLog1(tail,log_mode);
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else
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{
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//--- calculate cdf
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double pdf = MathExp(MathBinomialCoefficientLog(m-k,n)-MathBinomialCoefficientLog(m,n));
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double cdf = pdf;
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for(int j=0; j<=x_arg-1; j++)
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{
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pdf = pdf*(k-j)*(n-j)/((j+1)*(coef+j));
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cdf = cdf + pdf;
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}
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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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//| Hypergeometric 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 Hypergeometric distribution with parameters m,k,n for |
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//| the values in x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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 MathCumulativeDistributionHypergeometric(const double &x[],const double m,const double k,const double n,double &result[])
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{
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return MathCumulativeDistributionHypergeometric(x,m,k,n,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Hypergeometric distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| Computes the inverse cumulative distribution function of the |
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//| Hypergeometric distribution with parameters m,n,k for the |
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//| desired probability. |
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//| |
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//| Arguments: |
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//| probability : The probability |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode,if true it calculates for Log values|
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The smallest value x, such that the hypergeometric CDF(x) |
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//| equals or exceeds the desired probability. |
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//+------------------------------------------------------------------+
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//| Based on algorithm by John Burkardt |
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//+------------------------------------------------------------------+
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double MathQuantileHypergeometric(const double probability,const double m,const double k,const double n,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(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
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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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//--- m,k,n,x must be integer
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if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n))
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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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//--- m,k,n must be positive
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if(m<0 || k<0 || n<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 ranges
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if(n>m || k>m)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- calculate real probability
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double prob=TailLogProbability(probability,tail,log_mode);
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//--- check probability range
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if(prob<0.0 || prob>1.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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error_code=ERR_OK;
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//--- check probability
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if(prob==0)
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return 0.0;
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if(prob==1.0)
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return QPOSINF;
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int max_terms=1000;
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prob*=1-1000*DBL_EPSILON;
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double m_k=m-k;
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double pdf = MathExp(MathBinomialCoefficientLog(m_k,n)-MathBinomialCoefficientLog(m,n));
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double cdf = pdf;
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double coef=m_k-n+1;
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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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pdf = pdf*(k-j)*(n-j)/((j+1)*(coef+j));
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cdf = cdf + pdf;
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j++;
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}
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return j;
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}
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//+------------------------------------------------------------------+
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//| Hypergeometric distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| Computes the inverse cumulative distribution function of the |
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//| Hypergeometric distribution with parameters m,n,k for the |
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//| desired probability. |
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//| |
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//| Arguments: |
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//| probability : The probability |
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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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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 smallest value x, such that the hypergeometric CDF(x) |
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//| equals or exceeds the desired probability. |
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//+------------------------------------------------------------------+
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double MathQuantileHypergeometric(const double probability,const double m,const double k,const double n,int &error_code)
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{
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return MathQuantileHypergeometric(probability,m,k,n,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Hypergeometric 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 Hypergeometric distribution with parameters |
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//| m,k,n 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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//| m : Size of the population |
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//| k : Number of items with the desired characteristic |
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//| in the population |
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//| n : Number of samples drawn |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode,if true it calculates for Log values|
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|
//| result : Array with calculated values |
|
|
//| |
|
|
//| Return value: |
|
|
//| true if successful, otherwise false. |
|
|
//+------------------------------------------------------------------+
|
|
//| Based on algorithm by John Burkardt |
|
|
//+------------------------------------------------------------------+
|
|
bool MathQuantileHypergeometric(const double &probability[],const double m,const double k,const double n,const bool tail,const bool log_mode,double &result[])
|
|
{
|
|
//--- check NaN
|
|
if(!MathIsValidNumber(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
|
|
return false;
|
|
//--- m,k,n,x must be integer
|
|
if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n))
|
|
return false;
|
|
//--- m,k,n must be positive
|
|
if(m<0 || k<0 || n<0)
|
|
return false;
|
|
//--- check ranges
|
|
if(n>m || k>m)
|
|
return false;
|
|
|
|
int data_count=ArraySize(probability);
|
|
if(data_count==0)
|
|
return false;
|
|
|
|
int max_terms=1000;
|
|
double m_k=m-k;
|
|
double pdf0= MathExp(MathBinomialCoefficientLog(m_k,n)-MathBinomialCoefficientLog(m,n));
|
|
double coef=m_k-n+1;
|
|
|
|
ArrayResize(result,data_count);
|
|
for(int i=0; i<data_count; i++)
|
|
{
|
|
//--- calculate real probability
|
|
double prob=TailLogProbability(probability[i],tail,log_mode);
|
|
//--- check probability range
|
|
if(prob<0.0 || prob>1.0)
|
|
return false;
|
|
|
|
//--- check probability
|
|
if(prob==0.0)
|
|
result[i]=0.0;
|
|
else
|
|
if(prob==1.0)
|
|
result[i]=QPOSINF;
|
|
else
|
|
{
|
|
prob*=1-1000*DBL_EPSILON;
|
|
double pdf = pdf0;
|
|
double cdf = pdf;
|
|
int j=0;
|
|
while(cdf<prob && j<max_terms)
|
|
{
|
|
pdf = pdf*(k-j)*(n-j)/((j+1)*(coef+j));
|
|
cdf = cdf + pdf;
|
|
j++;
|
|
}
|
|
result[i]=j;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Hypergeometric distribution quantile function (inverse CDF) |
|
|
//+------------------------------------------------------------------+
|
|
//| The function calculates the inverse cumulative distribution |
|
|
//| function of the Hypergeometric distribution with parameters |
|
|
//| m,k,n for values from the probability[] array. |
|
|
//| |
|
|
//| Arguments: |
|
|
//| probability : Array with probabilities |
|
|
//| m : Size of the population |
|
|
//| k : Number of items with the desired characteristic |
|
|
//| in the population |
|
|
//| n : Number of samples drawn |
|
|
//| result : Array with calculated values |
|
|
//| |
|
|
//| Return value: |
|
|
//| true if successful, otherwise false. |
|
|
//+------------------------------------------------------------------+
|
|
bool MathQuantileHypergeometric(const double &probability[],const double m,const double k,const double n,double &result[])
|
|
{
|
|
return MathQuantileHypergeometric(probability,m,k,n,true,false,result);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Random variate from the Hypergeometric distribution |
|
|
//+------------------------------------------------------------------+
|
|
//| Compute the random variable from the Hypergeometric distribution |
|
|
//| with parameters m,n,k. |
|
|
//| |
|
|
//| Arguments: |
|
|
//| m : Size of the population |
|
|
//| k : Number of items with the desired characteristic |
|
|
//| in the population |
|
|
//| n : Number of samples drawn |
|
|
//| error_code : Variable for error code |
|
|
//| |
|
|
//| Return value: |
|
|
//| The random value with Hypergeometric distribution. |
|
|
//+------------------------------------------------------------------+
|
|
//| Author: John Burkardt |
|
|
//| |
|
|
//| Reference: |
|
|
//| Jerry Banks, editor, Handbook of Simulation, |
|
|
//| Engineering and Management Press Books, 1998, page 165. |
|
|
//+------------------------------------------------------------------+
|
|
double MathRandomHypergeometric(const double m,const double k,const double n,int &error_code)
|
|
{
|
|
//--- check NaN
|
|
if(!MathIsValidNumber(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
|
|
{
|
|
error_code=ERR_ARGUMENTS_NAN;
|
|
return QNaN;
|
|
}
|
|
//--- m,k,n,x must be integer
|
|
if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n))
|
|
{
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
|
return QNaN;
|
|
}
|
|
//--- m,k,n must be positive
|
|
if(m<0 || k<0 || n<0)
|
|
{
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
|
return QNaN;
|
|
}
|
|
//--- check ranges
|
|
if(n>m || k>m)
|
|
{
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
|
return QNaN;
|
|
}
|
|
|
|
error_code=ERR_OK;
|
|
//--- generate random number
|
|
double prob=MathRandomNonZero();
|
|
prob*=1-1000*DBL_EPSILON;
|
|
int max_terms=1000;
|
|
double m_k=m-k;
|
|
double coef=m_k-n+1;
|
|
double pdf= MathExp(MathBinomialCoefficientLog(m_k,n)-MathBinomialCoefficientLog(m,n));
|
|
double cdf= pdf;
|
|
int j=0;
|
|
while(cdf<prob && j<max_terms)
|
|
{
|
|
pdf = pdf*(k-j)*(n-j)/((j+1)*(coef+j));
|
|
cdf = cdf + pdf;
|
|
j++;
|
|
}
|
|
return j;
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Random variate from the Hypergeometric distribution |
|
|
//+------------------------------------------------------------------+
|
|
//| Generates random variables from the Hypergeometric distribution |
|
|
//| with parameters m,k,n. |
|
|
//| |
|
|
//| Arguments: |
|
|
//| m : Size of the population |
|
|
//| k : Number of items with the desired characteristic |
|
|
//| in the population |
|
|
//| n : Number of samples drawn |
|
|
//| data_count : Number of values needed |
|
|
//| result : Output array with random values |
|
|
//| |
|
|
//| Return value: |
|
|
//| true if successful, otherwise false. |
|
|
//+------------------------------------------------------------------+
|
|
bool MathRandomHypergeometric(const double m,const double k,const double n,const int data_count,double &result[])
|
|
{
|
|
//--- check NaN
|
|
if(!MathIsValidNumber(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
|
|
return false;
|
|
//--- m,k,n,x must be integer
|
|
if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n))
|
|
return false;
|
|
//--- m,k,n must be positive
|
|
if(m<0 || k<0 || n<0)
|
|
return false;
|
|
//--- check ranges
|
|
if(n>m || k>m)
|
|
return false;
|
|
//--- prepare coefficients
|
|
int max_terms=1000;
|
|
double m_k=m-k;
|
|
double coef=m_k-n+1;
|
|
double pdf0= MathExp(MathBinomialCoefficientLog(m_k,n)-MathBinomialCoefficientLog(m,n));
|
|
//--- prepare output array and calculate random values
|
|
ArrayResize(result,data_count);
|
|
for(int i=0; i<data_count; i++)
|
|
{
|
|
//--- generate random number
|
|
double prob=MathRandomNonZero();
|
|
prob*=1-1000*DBL_EPSILON;
|
|
//--- calculate using quantile
|
|
double pdf = pdf0;
|
|
double cdf = pdf;
|
|
int j=0;
|
|
while(cdf<prob && j<max_terms)
|
|
{
|
|
pdf = pdf*(k-j)*(n-j)/((j+1)*(coef+j));
|
|
cdf = cdf + pdf;
|
|
j++;
|
|
}
|
|
result[i]=j;
|
|
}
|
|
return true;
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| Hypergeometric distribution moments |
|
|
//+------------------------------------------------------------------+
|
|
//| The function calculates 4 first moments of the Hypergeometric |
|
|
//| distribution with parameters m,n,k. |
|
|
//| |
|
|
//| Arguments: |
|
|
//| m : Size of the population |
|
|
//| k : Number of items with the desired characteristic |
|
|
//| in the population |
|
|
//| n : Number of samples drawn |
|
|
//| 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 MathMomentsHypergeometric(const double m,const double k,const double n,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(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
|
|
{
|
|
error_code=ERR_ARGUMENTS_NAN;
|
|
return false;
|
|
}
|
|
//--- m,k,n must be integer
|
|
if(m!=MathRound(m) || k!=MathRound(k) || n!=MathRound(n))
|
|
{
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
|
return false;
|
|
}
|
|
//--- m,k,n must be positive
|
|
if(m<0 || k<0 || n<0)
|
|
{
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
|
return false;
|
|
}
|
|
//--- check ranges
|
|
if(n>m || k>m)
|
|
{
|
|
error_code=ERR_ARGUMENTS_INVALID;
|
|
return false;
|
|
}
|
|
|
|
error_code=ERR_OK;
|
|
//--- calculate moments
|
|
mean =n*k/m;
|
|
variance=k*n*(1-k/m)*(m-n)/(m*(m-1));
|
|
skewness=MathSqrt(m-1)*(m-2*k)*(m-2*n)/((m-2)*MathSqrt(k*n*(m-k)*(m-n)));
|
|
kurtosis=(m-1)*m*m/(k*n*(m-3)*(m-2)*(m-k)*(m-n));
|
|
kurtosis*=3*k*(m-k)*(m*m*(n-2)-m*n*n+6*n*(m-n))/(m*m)-6*n*(m-n)+m*(m+1);
|
|
kurtosis-=3;
|
|
//--- successful
|
|
return true;
|
|
}
|
|
//+------------------------------------------------------------------+
|