| //+------------------------------------------------------------------+
|
| //| Hypergeometric.mqh |
|
| //| Copyright 2000-2025, MetaQuotes Ltd. |
|
| //| https://www.mql5.com |
|
| //+------------------------------------------------------------------+
|
| #include "Math.mqh"
|
|
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric probability mass function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability mass function |
|
| //| of the Hypergeometric distribution with parameters m,n,k. |
|
| //| f(x,m,k,n)=C(k,x)*C(m-k,n-x)/C(m,n) |
|
| //| where binomial coefficient C(n,k)=n!/(k!*(n-k)! |
|
| //| |
|
| //| Arguments: |
|
| //| x : The desired number of objects |
|
| //| m : Size of the population |
|
| //| k : Number of items with the desired characteristic |
|
| //| in the population |
|
| //| n : Number of samples drawn |
|
| //| log_mode : Logarithm mode flag, if true it returns Log values |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The probability mass function, evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathProbabilityDensityHypergeometric(const double x,const double m,const double k,const double n,const bool log_mode,int &error_code)
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(x) || !MathIsValidNumber(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
|
| {
|
| error_code=ERR_ARGUMENTS_NAN;
|
| return(QNaN);
|
| }
|
| //--- m,k,n 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;
|
| //--- check ranges
|
| if(x>n)
|
| return TailLog0(true,log_mode);
|
| if(x>k || m-k-n+x+1<=0)
|
| return TailLog0(true,log_mode);
|
| //--- calculate log binomial coefficients
|
| double log_pdf=MathBinomialCoefficientLog(k,x)+MathBinomialCoefficientLog(m-k,n-x)-MathBinomialCoefficientLog(m,n);
|
| if(log_mode==true)
|
| return log_pdf;
|
| //--- return hypergeometric density
|
| return MathExp(log_pdf);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric probability mass function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability mass function |
|
| //| of the Hypergeometric distribution with parameters m,n,k. |
|
| //| f(x,m,k,n)=C(k,x)*C(m-k,n-x)/C(m,n) |
|
| //| where binomial coefficient C(n,k)=n!/(k!*(n-k)! |
|
| //| |
|
| //| Arguments: |
|
| //| x : The desired number of objects |
|
| //| 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 probability mass function, evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathProbabilityDensityHypergeometric(const double x,const double m,const double k,const double n,int &error_code)
|
| {
|
| return MathProbabilityDensityHypergeometric(x,m,k,n,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric probability mass function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the probability mass function of the |
|
| //| Hypergeometric distribution with parameter m,k,n for values in x.|
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| x : The desired number of objects |
|
| //| m : Size of the population |
|
| //| k : Number of items with the desired characteristic |
|
| //| in the population |
|
| //| n : Number of samples drawn |
|
| //| log_mode : Logarithm mode, if true it calculates Log values |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathProbabilityDensityHypergeometric(const double &x[],const double m,const double k,const double n,const bool log_mode,double &result[])
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(m) || !MathIsValidNumber(k) || !MathIsValidNumber(n))
|
| return false;
|
| //--- m,k,n 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(x);
|
| if(data_count==0)
|
| return false;
|
|
|
| double m_k=m-k;
|
| int error_code=0;
|
| ArrayResize(result,data_count);
|
| for(int i=0; i<data_count; i++)
|
| {
|
| double x_arg=x[i];
|
|
|
| if(!MathIsValidNumber(x_arg))
|
| return false;
|
|
|
| if(x_arg<0 || x_arg!=MathRound(x_arg))
|
| return false;
|
|
|
| if(x_arg>n)
|
| result[i]=TailLog0(true,log_mode);
|
| else
|
| //--- check ranges
|
| if(x_arg>k || m_k-n+x_arg+1<=0)
|
| result[i]=TailLog0(true,log_mode);
|
| else
|
| {
|
| //--- calculate log binomial coefficients
|
| double log_pdf=MathBinomialCoefficientLog(k,x_arg)+MathBinomialCoefficientLog(m_k,n-x_arg)-MathBinomialCoefficientLog(m,n);
|
| if(log_mode==true)
|
| result[i]=log_pdf;
|
| else
|
| result[i]=MathExp(log_pdf);
|
| }
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric probability mass function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the probability mass function of the |
|
| //| Hypergeometric distribution with parameter m,k,n for values in x.|
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| x : The desired number of objects |
|
| //| 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 MathProbabilityDensityHypergeometric(const double &x[],const double m,const double k,const double n,double &result[])
|
| {
|
| return MathProbabilityDensityHypergeometric(x,m,k,n,false,result);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability that an observation |
|
| //| from the Hypergeometric distribution with parameters m,n,k |
|
| //| is less than or equal to x. |
|
| //| |
|
| //| Arguments: |
|
| //| x : The desired number of objects |
|
| //| m : Size of the population |
|
| //| k : Number of items with the desired characteristic |
|
| //| in the population |
|
| //| n : Number of samples drawn |
|
| //| tail : Flag to calculate lower tail |
|
| //| log_mode : Logarithm mode,if true it calculates Log values |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The value of the Hypergeometric cumulative distribution function |
|
| //| with parameters m,n,k, evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| //| Based on algorithm by John Burkardt |
|
| //+------------------------------------------------------------------+
|
| double MathCumulativeDistributionHypergeometric(const double x,const double m,const double k,const double n,const bool tail,const bool log_mode,int &error_code)
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(x) || !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) || x!=MathRound(x))
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
| //--- m,k,n,x must be positive
|
| if(m<0 || k<0 || n<0 || x<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;
|
| if(x>=n || x>=k)
|
| return TailLog1(tail,log_mode);
|
| //--- calculate cdf
|
| double pdf = MathExp(MathBinomialCoefficientLog(m-k,n)-MathBinomialCoefficientLog(m,n));
|
| double cdf = pdf;
|
| double coef=m-k-n+1;
|
| for(int j=0; j<=x-1; j++)
|
| {
|
| pdf = pdf*(k-j)*(n-j)/((j+1)*(coef+j));
|
| cdf = cdf + pdf;
|
| }
|
| return TailLogValue(MathMin(cdf,1.0),tail,log_mode);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability that an observation |
|
| //| from the Hypergeometric distribution with parameters m,n,k |
|
| //| is less than or equal to x. |
|
| //| |
|
| //| Arguments: |
|
| //| x : The desired number of objects |
|
| //| 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 value of the Hypergeometric cumulative distribution function |
|
| //| with parameters m,n,k, evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathCumulativeDistributionHypergeometric(const double x,const double m,const double k,const double n,int &error_code)
|
| {
|
| return MathCumulativeDistributionHypergeometric(x,m,k,n,true,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the cumulative distribution function of |
|
| //| the Hypergeometric distribution with parameters m,k,n for |
|
| //| the values in x[] array. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| m : Size of the population |
|
| //| k : Number of items with the desired characteristic |
|
| //| in the population |
|
| //| n : Number of samples drawn |
|
| //| tail : Flag to calculate lower tail |
|
| //| log_mode : Logarithm mode,if true it calculates Log values |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| //| Based on algorithm by John Burkardt |
|
| //+------------------------------------------------------------------+
|
| bool MathCumulativeDistributionHypergeometric(const double &x[],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(x);
|
| if(data_count==0)
|
| return false;
|
|
|
| double coef=m-k-n+1;
|
|
|
| ArrayResize(result,data_count);
|
| for(int i=0; i<data_count; i++)
|
| {
|
| double x_arg=x[i];
|
|
|
| if(!MathIsValidNumber(x_arg))
|
| return false;
|
|
|
| //--- x must be positive and integer
|
| if(x_arg<0 || x_arg!=MathRound(x_arg))
|
| return false;
|
|
|
| //--- check ranges
|
| if(x_arg>=n || x_arg>=k)
|
| result[i]=TailLog1(tail,log_mode);
|
| else
|
| {
|
| //--- calculate cdf
|
| double pdf = MathExp(MathBinomialCoefficientLog(m-k,n)-MathBinomialCoefficientLog(m,n));
|
| double cdf = pdf;
|
| for(int j=0; j<=x_arg-1; j++)
|
| {
|
| pdf = pdf*(k-j)*(n-j)/((j+1)*(coef+j));
|
| cdf = cdf + pdf;
|
| }
|
| result[i]=TailLogValue(MathMin(cdf,1.0),tail,log_mode);
|
| }
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the cumulative distribution function of |
|
| //| the Hypergeometric distribution with parameters m,k,n for |
|
| //| the values in x[] array. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| 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 MathCumulativeDistributionHypergeometric(const double &x[],const double m,const double k,const double n,double &result[])
|
| {
|
| return MathCumulativeDistributionHypergeometric(x,m,k,n,true,false,result);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric distribution quantile function (inverse CDF) |
|
| //+------------------------------------------------------------------+
|
| //| Computes the inverse cumulative distribution function of the |
|
| //| Hypergeometric distribution with parameters m,n,k for the |
|
| //| desired probability. |
|
| //| |
|
| //| Arguments: |
|
| //| probability : The probability |
|
| //| m : Size of the population |
|
| //| k : Number of items with the desired characteristic |
|
| //| in the population |
|
| //| n : Number of samples drawn |
|
| //| tail : Flag to calculate lower tail |
|
| //| log_mode : Logarithm mode,if true it calculates for Log values|
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The smallest value x, such that the hypergeometric CDF(x) |
|
| //| equals or exceeds the desired probability. |
|
| //+------------------------------------------------------------------+
|
| //| Based on algorithm by John Burkardt |
|
| //+------------------------------------------------------------------+
|
| double MathQuantileHypergeometric(const double probability,const double m,const double k,const double n,const bool tail,const bool log_mode,int &error_code)
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(probability) || !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;
|
| }
|
| //--- calculate real probability
|
| double prob=TailLogProbability(probability,tail,log_mode);
|
| //--- check probability range
|
| if(prob<0.0 || prob>1.0)
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
|
|
| error_code=ERR_OK;
|
| //--- check probability
|
| if(prob==0)
|
| return 0.0;
|
| if(prob==1.0)
|
| return QPOSINF;
|
|
|
| int max_terms=1000;
|
| prob*=1-1000*DBL_EPSILON;
|
| double m_k=m-k;
|
| double pdf = MathExp(MathBinomialCoefficientLog(m_k,n)-MathBinomialCoefficientLog(m,n));
|
| double cdf = pdf;
|
| double coef=m_k-n+1;
|
| 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;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Hypergeometric distribution quantile function (inverse CDF) |
|
| //+------------------------------------------------------------------+
|
| //| Computes the inverse cumulative distribution function of the |
|
| //| Hypergeometric distribution with parameters m,n,k for the |
|
| //| desired probability. |
|
| //| |
|
| //| Arguments: |
|
| //| probability : The probability |
|
| //| 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 smallest value x, such that the hypergeometric CDF(x) |
|
| //| equals or exceeds the desired probability. |
|
| //+------------------------------------------------------------------+
|
| double MathQuantileHypergeometric(const double probability,const double m,const double k,const double n,int &error_code)
|
| {
|
| return MathQuantileHypergeometric(probability,m,k,n,true,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| 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 |
|
| //| tail : Flag to calculate lower tail |
|
| //| log_mode : Logarithm mode,if true it calculates for Log values|
|
| //| 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. |
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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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| //| 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 MathQuantileHypergeometric(const double &probability[],const double m,const double k,const double n,double &result[])
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| {
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| return MathQuantileHypergeometric(probability,m,k,n,true,false,result);
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| }
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| //+------------------------------------------------------------------+
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| //| Random variate from the Hypergeometric distribution |
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| //+------------------------------------------------------------------+
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| //| Compute the random variable from the Hypergeometric distribution |
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| //| with parameters m,n,k. |
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| //| |
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| //| Arguments: |
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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 random value with Hypergeometric distribution. |
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| //+------------------------------------------------------------------+
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| //| Author: John Burkardt |
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| //| |
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| //| Reference: |
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| //| Jerry Banks, editor, Handbook of Simulation, |
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| //| Engineering and Management Press Books, 1998, page 165. |
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| //+------------------------------------------------------------------+
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| double MathRandomHypergeometric(const double m,const double k,const double n,int &error_code)
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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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| {
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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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|
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| error_code=ERR_OK;
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| //--- generate random number
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| double prob=MathRandomNonZero();
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| prob*=1-1000*DBL_EPSILON;
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| int max_terms=1000;
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| double m_k=m-k;
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| double coef=m_k-n+1;
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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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| 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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| //| Random variate from the Hypergeometric distribution |
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| //+------------------------------------------------------------------+
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| //| Generates random variables from the Hypergeometric distribution |
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| //| with parameters m,k,n. |
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| //| |
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| //| Arguments: |
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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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| //| data_count : Number of values needed |
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| //| result : Output array with random values |
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| //| |
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| //| Return value: |
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| //| true if successful, otherwise false. |
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| //+------------------------------------------------------------------+
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| bool MathRandomHypergeometric(const double m,const double k,const double n,const int data_count,double &result[])
|
| {
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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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| //--- prepare coefficients
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| int max_terms=1000;
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| double m_k=m-k;
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| double coef=m_k-n+1;
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| double pdf0= MathExp(MathBinomialCoefficientLog(m_k,n)-MathBinomialCoefficientLog(m,n));
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| //--- prepare output array and calculate random values
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| ArrayResize(result,data_count);
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| for(int i=0; i<data_count; i++)
|
| {
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| //--- generate random number
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| double prob=MathRandomNonZero();
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| prob*=1-1000*DBL_EPSILON;
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| //--- calculate using quantile
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| double pdf = pdf0;
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| double cdf = pdf;
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| int j=0;
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| while(cdf<prob && j<max_terms)
|
| {
|
| 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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| result[i]=j;
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
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| //| Hypergeometric distribution moments |
|
| //+------------------------------------------------------------------+
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| //| The function calculates 4 first moments of the Hypergeometric |
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| //| distribution with parameters m,n,k. |
|
| //| |
|
| //| Arguments: |
|
| //| m : Size of the population |
|
| //| k : Number of items with the desired characteristic |
|
| //| in the population |
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| //| n : Number of samples drawn |
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| //| mean : Variable for mean value (1st moment) |
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| //| variance : Variable for variance value (2nd moment) |
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| //| skewness : Variable for skewness value (3rd moment) |
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| //| kurtosis : Variable for kurtosis value (4th moment) |
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| //| error_code : Variable for error code |
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| //| |
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| //| Return value: |
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| //| 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
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| mean =QNaN;
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| variance=QNaN;
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| skewness=QNaN;
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| 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));
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| 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;
|
| }
|
| //+------------------------------------------------------------------+
|
