First commit [09/03/2018]
This commit is contained in:
Pierre8rTeam
@@ -0,0 +1,793 @@
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//+------------------------------------------------------------------+
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//| Poisson.mqh |
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//| Copyright 2016-2017, MetaQuotes Software Corp. |
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//| https://www.mql5.com |
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//+------------------------------------------------------------------+
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#property copyright "Copyright 2016-2017, MetaQuotes Software Corp."
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#property link "https://www.mql5.com"
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#include "Math.mqh"
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#include "Gamma.mqh"
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//+------------------------------------------------------------------+
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//| Poisson 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 Poisson distribution with parameter lambda. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| lambda : Mean |
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//| log_mode : Logarithm mode flag, if true it returns Log values |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The probability mass evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityPoisson(const double x,const double lambda,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(lambda))
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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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//--- lambda must be positive, x must be integer
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if(lambda<=0.0 || 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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error_code=ERR_OK;
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//--- check x
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if(x<0.0)
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return TailLog0(true,log_mode);
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//--- calculate log pdf using LogGamma
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double log_pdf=-lambda+x*MathLog(lambda)-MathGammaLog(x+1.0);
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if(log_mode)
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return log_pdf;
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//--- return density
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return MathExp(log_pdf);
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}
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//+------------------------------------------------------------------+
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//| Poisson 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 Poisson distribution with parameter lambda. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| lambda : Mean |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The probability mass evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityPoisson(const double x,const double lambda,int &error_code)
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{
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return MathProbabilityDensityPoisson(x,lambda,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Poisson probability mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of |
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//| the Poisson distribution with parameter lambda 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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//| lambda : Mean |
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//| log_mode : Logarithm mode flag, if true it returns Log values |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathProbabilityDensityPoisson(const double &x[],const double lambda,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(lambda))
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return false;
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//--- lambda must be positive
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if(lambda<=0.0)
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return false;
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int data_count=ArraySize(x);
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if(data_count==0)
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return false;
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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!=MathRound(x_arg))
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return false;
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//--- check x
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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 log pdf using LogGamma
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double log_pdf=-lambda+x_arg*MathLog(lambda)-MathGammaLog(x_arg+1.0);
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if(log_mode)
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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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//| Poisson probability mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of |
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//| the Poisson distribution with parameter lambda 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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//| lambda : Mean |
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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 MathProbabilityDensityPoisson(const double &x[],const double lambda,double &result[])
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{
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return MathProbabilityDensityPoisson(x,lambda,false,result);
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}
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//+------------------------------------------------------------------+
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//| Poisson 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 Poisson distribution with parameter lambda |
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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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//| lambda : Mean |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode, if true it calculates Log values |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of the Poisson cumulative distribution function with |
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//| parameter lambda, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionPoisson(const double x,const double lambda,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(lambda))
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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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//--- lambda must be positive, x must be integer
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if(lambda<=0.0 || 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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error_code=ERR_OK;
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//--- check x
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if(x<0.0)
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return TailLog0(tail,log_mode);
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int err_code=0;
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int t=(int)MathFloor(x+10e-10);
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double cdf=MathCumulativeDistributionGamma(lambda,t+1,1,false,false,err_code);
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return TailLogValue(cdf,tail,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Poisson 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 Poisson distribution with parameter lambda |
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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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//| lambda : Mean |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of the Poisson cumulative distribution function with |
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//| parameter lambda, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionPoisson(const double x,const double lambda,int &error_code)
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{
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return MathCumulativeDistributionPoisson(x,lambda,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Poisson 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 Poisson distribution with parameter lambda 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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//| lambda : Mean |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode, if true it calculates Log values |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathCumulativeDistributionPoisson(const double &x[],const double lambda,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(lambda))
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return false;
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//--- lambda must be positive
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if(lambda<=0.0)
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return false;
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int data_count=ArraySize(x);
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if(data_count==0)
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return false;
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int error_code=0;
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ArrayResize(result,data_count);
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double coef_lambda=MathExp(-lambda);
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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(x_arg!=MathRound(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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int t=(int)MathFloor(x_arg+10e-10);
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double cdf=MathCumulativeDistributionGamma(lambda,t+1,1,false,false,err_code);
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result[i]=TailLogValue(cdf,tail,log_mode);
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}
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Poisson 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 Poisson distribution with parameter lambda 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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//| lambda : Mean |
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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 MathCumulativeDistributionPoisson(const double &x[],const double lambda,double &result[])
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{
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return MathCumulativeDistributionPoisson(x,lambda,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Poisson 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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//| Poisson distribution with parameter lambda for the desired |
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//| probability. |
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//| |
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//| Arguments: |
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//| probability : The desired probability |
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//| lambda : Mean |
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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 value of the inverse cumulative distribution function |
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//| of the Poisson distribution with parameter lambda. |
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//+------------------------------------------------------------------+
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double MathQuantilePoisson(const double probability,const double lambda,const bool tail,const bool log_mode,int &error_code)
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{
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//--- check parameters
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if(!MathIsValidNumber(probability) || !MathIsValidNumber(lambda))
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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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//--- lambda must be positive
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if(lambda<=0.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- calculate real probability
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double prob=TailLogProbability(probability,tail,log_mode);
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//--- check probability range
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if(prob<0.0 || prob>1.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- check
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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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prob*=1-1000*DBL_EPSILON;
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int err_code=0;
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int j=0;
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const int max_terms=500;
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double coef_lambda=MathExp(-lambda);
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double pwr_lambda=1.0;
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double inverse_fact=1.0;
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double sum=0;
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//--- direct calculation of the quantile
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while(sum<prob && j<max_terms)
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{
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if(j>0)
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{
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pwr_lambda*=lambda;
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inverse_fact/=j;
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}
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sum+=coef_lambda*pwr_lambda*inverse_fact;
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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_RESULT_INFINITE;
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return QPOSINF;
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}
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}
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//+------------------------------------------------------------------+
|
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//| Poisson 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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//| Poisson distribution with parameter lambda for the desired |
|
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//| probability. |
|
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//| |
|
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//| Arguments: |
|
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//| probability : The desired probability |
|
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//| lambda : Mean |
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//| error_code : Variable for error code |
|
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//| |
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//| Return value: |
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//| The value of the inverse cumulative distribution function |
|
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//| of Poisson distribution with parameter lambda. |
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//+------------------------------------------------------------------+
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double MathQuantilePoisson(const double probability,const double lambda,int &error_code)
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{
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return MathQuantilePoisson(probability,lambda,true,false,error_code);
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}
|
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//+------------------------------------------------------------------+
|
||||
//| Poisson distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates the inverse cumulative distribution |
|
||||
//| function of the Poisson distribution with parameter lambda |
|
||||
//| for values from the probability[] array. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| probability : Array with probabilities |
|
||||
//| lambda : Mean |
|
||||
//| 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. |
|
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//+------------------------------------------------------------------+
|
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bool MathQuantilePoisson(const double &probability[],const double lambda,const bool tail,const bool log_mode,double &result[])
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{
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//--- NaN
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if(!MathIsValidNumber(lambda))
|
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return false;
|
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//--- lambda must be positive
|
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if(lambda<=0.0)
|
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return false;
|
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|
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int data_count=ArraySize(probability);
|
||||
if(data_count==0)
|
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return false;
|
||||
|
||||
int error_code=0;
|
||||
ArrayResize(result,data_count);
|
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double coef_lambda=MathExp(-lambda);
|
||||
|
||||
for(int i=0; i<data_count; i++)
|
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{
|
||||
//--- calculate real probability
|
||||
double prob=TailLogProbability(probability[i],tail,log_mode);
|
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|
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//--- check probability range
|
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if(prob<0.0 || prob>1.0)
|
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return false;
|
||||
else
|
||||
if(prob==1.0)
|
||||
result[i]=QPOSINF;
|
||||
if(prob==0.0)
|
||||
result[i]=0;
|
||||
else
|
||||
{
|
||||
prob*=1-1000*DBL_EPSILON;
|
||||
int err_code=0;
|
||||
int j=0;
|
||||
double sum=0.0;
|
||||
const int max_terms=500;
|
||||
double pwr_lambda=1.0;
|
||||
double inverse_fact=1.0;
|
||||
//--- direct calculation
|
||||
while(sum<prob && j<max_terms)
|
||||
{
|
||||
if(j>0)
|
||||
{
|
||||
pwr_lambda*=lambda;
|
||||
inverse_fact/=j;
|
||||
}
|
||||
sum+=coef_lambda*pwr_lambda*inverse_fact;
|
||||
j++;
|
||||
}
|
||||
//--- check convergence
|
||||
if(j<max_terms)
|
||||
{
|
||||
if(j==0)
|
||||
result[i]=0;
|
||||
else
|
||||
result[i]=j-1;
|
||||
}
|
||||
else
|
||||
return false;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Poisson distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates the inverse cumulative distribution |
|
||||
//| function of the Poisson distribution with parameter lambda |
|
||||
//| for values from the probability[] array. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| probability : Array with probabilities |
|
||||
//| lambda : Mean |
|
||||
//| result : Array with calculated values |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if successful, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathQuantilePoisson(const double &probability[],const double lambda,double &result[])
|
||||
{
|
||||
return MathQuantilePoisson(probability,lambda,true,false,result);
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Poisson distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Compute the random variable from the Poisson distribution |
|
||||
//| with parameter lambda. |
|
||||
//| |
|
||||
//| Arguments |
|
||||
//| lambda : Mean |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| The random value with Poisson distribution. |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Original FORTRAN77 version by Barry Brown, James Lovato. |
|
||||
//| C version by John Burkardt. |
|
||||
//| |
|
||||
//| Reference: |
|
||||
//| Joachim Ahrens, Ulrich Dieter, "Computer Generation of Poisson |
|
||||
//| "Deviates From Modified Normal Distributions", |
|
||||
//| ACM Transactions on Mathematical Software, |
|
||||
//| Volume 8, Number 2, June 1982, pages 163-179. |
|
||||
//+------------------------------------------------------------------+
|
||||
double MathRandomPoisson(const double lambda)
|
||||
{
|
||||
const double a0 = -0.5;
|
||||
const double a1 = 0.3333333;
|
||||
const double a2 = -0.2500068;
|
||||
const double a3 = 0.2000118;
|
||||
const double a4 = -0.1661269;
|
||||
const double a5 = 0.1421878;
|
||||
const double a6 = -0.1384794;
|
||||
const double a7 = 0.1250060;
|
||||
int kflag;
|
||||
double fk=0,difmuk=0;
|
||||
double e=0,fx,fy,g,p0,px,py,p,q,s,t,u=0,v,x,xx;
|
||||
int value=0;
|
||||
//--- start new table and calculate P0
|
||||
if(lambda<10.0)
|
||||
{
|
||||
int m=MathMax(1,(int)(lambda));
|
||||
p = MathExp(-lambda);
|
||||
q = p;
|
||||
p0= p;
|
||||
//--- uniform sample for inversion method
|
||||
for(;;)
|
||||
{
|
||||
u=MathRandomNonZero();
|
||||
value=0;
|
||||
|
||||
if(u<=p0)
|
||||
return value;
|
||||
//--- creation of new Poisson probabilities
|
||||
for(int k=1; k<=35; k++)
|
||||
{
|
||||
p=p*lambda/double(k);
|
||||
q=q+p;
|
||||
if(u<=q)
|
||||
{
|
||||
value=k;
|
||||
return value;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
s=MathSqrt(lambda);
|
||||
double d=6.0*lambda*lambda;
|
||||
int l=(int)(lambda-1.1484);
|
||||
//--- generate normal deviate
|
||||
double f,x1,x2,r2;
|
||||
do
|
||||
{
|
||||
x1=2.0*MathRandomNonZero()-1.0;
|
||||
x2=2.0*MathRandomNonZero()-1.0;
|
||||
r2=x1*x1+x2*x2;
|
||||
}
|
||||
while(r2>=1.0 || r2==0.0);
|
||||
//--- Box-Muller transform
|
||||
f=MathSqrt(-2.0*MathLog(r2)/r2);
|
||||
double snorm=f*x2;
|
||||
//--- normal sample
|
||||
g=lambda+s*snorm;
|
||||
|
||||
if(0.0<=g)
|
||||
{
|
||||
value=(int)(g);
|
||||
//--- immediate acceptance if large enough
|
||||
if(l<=value)
|
||||
return value;
|
||||
//--- squeeze acceptance
|
||||
fk=(double)(value);
|
||||
difmuk=lambda-fk;
|
||||
u=MathRandomNonZero();
|
||||
//---
|
||||
if(difmuk*difmuk*difmuk<=d*u)
|
||||
return value;
|
||||
}
|
||||
//--- preparation for steps P and Q
|
||||
double omega=0.3989423/s;
|
||||
double b1 = 0.04166667/lambda;
|
||||
double b2 = 0.3*b1*b1;
|
||||
double c3 = 0.1428571*b1*b2;
|
||||
double c2 = b2 - 15.0*c3;
|
||||
double c1 = b1 - 6.0*b2 + 45.0*c3;
|
||||
double c0 = 1.0 - b1 + 3.0*b2 - 15.0*c3;
|
||||
double c=0.1069/lambda;
|
||||
double del=0;
|
||||
|
||||
if(0.0<=g)
|
||||
{
|
||||
kflag=0;
|
||||
|
||||
if(value<10)
|
||||
{
|
||||
px = -lambda;
|
||||
py = MathPow(lambda,value)/MathFactorial(value);
|
||||
}
|
||||
else
|
||||
{
|
||||
del = 0.8333333E-01/fk;
|
||||
del = del - 4.8*del*del*del;
|
||||
v=difmuk/fk;
|
||||
|
||||
if(0.25<MathAbs(v))
|
||||
{
|
||||
px=fk*MathLog(1.0+v)-difmuk-del;
|
||||
}
|
||||
else
|
||||
{
|
||||
px=fk*v*v*(((((((a7*v+a6)*v+a5)*v+a4)*v+a3)*v+a2)*v+a1)*v+a0)-del;
|
||||
}
|
||||
py=0.3989423/MathSqrt(fk);
|
||||
}
|
||||
x=(0.5-difmuk)/s;
|
||||
xx = x * x;
|
||||
fx = -0.5 * xx;
|
||||
fy = omega*(((c3*xx+c2)*xx+c1)*xx+c0);
|
||||
|
||||
if(kflag<=0)
|
||||
{
|
||||
if(fy-u*fy<=py*MathExp(px-fx))
|
||||
return value;
|
||||
}
|
||||
else
|
||||
{
|
||||
if(c*MathAbs(u)<=py*MathExp(px+e)-fy*MathExp(fx+e))
|
||||
return value;
|
||||
}
|
||||
}
|
||||
//--- exponential sample
|
||||
for(;;)
|
||||
{
|
||||
double rnd=MathRandomNonZero();
|
||||
e=-MathLog(1.0-rnd);
|
||||
|
||||
u=2.0*MathRandomNonZero()-1.0;
|
||||
if(u<0.0)
|
||||
t=1.8-MathAbs(e);
|
||||
else
|
||||
t=1.8+MathAbs(e);
|
||||
|
||||
if(t<=-0.6744)
|
||||
continue;
|
||||
|
||||
value=(int)(lambda+s*t);
|
||||
fk=(double)(value);
|
||||
difmuk=lambda-fk;
|
||||
|
||||
kflag=1;
|
||||
//--- calculation of PX, PY, FX, FY
|
||||
if(value<10)
|
||||
{
|
||||
px = -lambda;
|
||||
py = MathPow(lambda,value)/MathFactorial(value);
|
||||
}
|
||||
else
|
||||
{
|
||||
del = 0.8333333E-01/fk;
|
||||
del = del - 4.8*del*del*del;
|
||||
v=difmuk/fk;
|
||||
|
||||
if(0.25<MathAbs(v))
|
||||
px=fk*MathLog(1.0+v)-difmuk-del;
|
||||
else
|
||||
px=fk*v*v*(((((((a7*v+a6)*v+a5)*v+a4)*v+a3)*v+a2)*v+a1)*v+a0)-del;
|
||||
|
||||
py=0.3989423/MathSqrt(fk);
|
||||
}
|
||||
|
||||
x=(0.5-difmuk)/s;
|
||||
xx = x*x;
|
||||
fx = -0.5*xx;
|
||||
fy = omega*(((c3*xx+c2)*xx+c1)*xx+c0);
|
||||
|
||||
if(kflag<=0)
|
||||
{
|
||||
if(fy-u*fy<=py*MathExp(px-fx))
|
||||
return value;
|
||||
}
|
||||
else
|
||||
{
|
||||
if(c*MathAbs(u)<=py*MathExp(px+e)-fy*MathExp(fx+e))
|
||||
return value;
|
||||
}
|
||||
}
|
||||
}
|
||||
return value;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Poisson distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Compute the random variable from the Poisson distribution |
|
||||
//| with parameter lambda. |
|
||||
//| |
|
||||
//| Arguments |
|
||||
//| lambda : Mean |
|
||||
//| error_code : Variable for error code |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| The random value with Poisson distribution. |
|
||||
//+------------------------------------------------------------------+
|
||||
double MathRandomPoisson(const double lambda,int &error_code)
|
||||
{
|
||||
//--- check parameters
|
||||
if(!MathIsValidNumber(lambda))
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_NAN;
|
||||
return QNaN;
|
||||
}
|
||||
//--- lambda must be positive
|
||||
if(lambda<=0.0)
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_INVALID;
|
||||
return QNaN;
|
||||
}
|
||||
error_code=ERR_OK;
|
||||
return MathRandomPoisson(lambda);
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Poisson distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Generates random variables from the Poisson distribution |
|
||||
//| with parameter lambda. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| lambda : Mean |
|
||||
//| data_count : Number of values needed |
|
||||
//| result : Output array with random values |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if successful, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathRandomPoisson(const double lambda,const int data_count,double &result[])
|
||||
{
|
||||
//--- check NaN
|
||||
if(!MathIsValidNumber(lambda))
|
||||
return false;
|
||||
//--- lambda must be positive
|
||||
if(lambda<=0.0)
|
||||
return false;
|
||||
//--- prepare output array and calculate random values
|
||||
ArrayResize(result,data_count);
|
||||
for(int i=0; i<data_count; i++)
|
||||
{
|
||||
result[i]=MathRandomPoisson(lambda);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Poisson distribution moments |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates 4 first moments of the Poisson |
|
||||
//| distribution with parameter lambda. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| lambda : Mean |
|
||||
//| mean : Variable for mean value (1st moment) |
|
||||
//| variance : Variable for variance value (2nd moment) |
|
||||
//| skewness : Variable for skewness value (3rd moment) |
|
||||
//| kurtosis : Variable for kurtosis value (4th moment) |
|
||||
//| error_code : Variable for error code |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if moments calculated successfully, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathMomentsPoisson(const double lambda,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(lambda))
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_NAN;
|
||||
return false;
|
||||
}
|
||||
//--- lambda must be positive
|
||||
if(lambda<=0.0)
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_INVALID;
|
||||
return false;
|
||||
}
|
||||
|
||||
error_code=ERR_OK;
|
||||
//--- calculate moments
|
||||
mean =lambda;
|
||||
variance=lambda;
|
||||
skewness=MathPow(lambda,-0.5);
|
||||
kurtosis=1.0/lambda;
|
||||
//--- successful
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
Reference in New Issue
Block a user