First commit [09/03/2018]
This commit is contained in:
Pierre8rTeam
@@ -0,0 +1,569 @@
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//+------------------------------------------------------------------+
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//| Geometric.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 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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//+------------------------------------------------------------------+
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//| Geometric mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability mass function of the |
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//| Geometric distribution with parameter p. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| p : Probability parameter |
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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 MathProbabilityDensityGeometric(const double x,const double p,const bool log_mode,int &error_code)
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{
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//--- check NaN
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if(!MathIsValidNumber(x) || !MathIsValidNumber(p))
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{
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error_code=ERR_ARGUMENTS_NAN;
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return QNaN;
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}
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//--- check probability
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if(p<=0.0 || p>1.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- check x
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if(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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if(x<0)
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return TailLog0(true,log_mode);
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if(p==1.0)
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{
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if(x==0.0)
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return TailLog1(true,log_mode);
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else
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return TailLog0(true,log_mode);
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}
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//--- return geometric density
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return TailLogValue(p*MathPow(1.0-p,x),true,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Geometric mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability mass function of |
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//| the Geometric distribution with parameter p. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| p : Probability parameter |
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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 MathProbabilityDensityGeometric(const double x,const double p,int &error_code)
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{
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return MathProbabilityDensityGeometric(x,p,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Geometric mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability mass function of |
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//| the Geometric distribution with parameter p 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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//| p : Probability parameter |
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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 MathProbabilityDensityGeometric(const double &x[],const double p,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(p))
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return false;
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//--- check probability
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if(p<=0.0 || p>1.0)
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return false;
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int data_count=ArraySize(x);
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if(data_count==0)
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return false;
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int error_code=0;
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ArrayResize(result,data_count);
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//--- special case p==1.0
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if(p==1.0)
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{
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for(int i=0; i<data_count; i++)
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{
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if(x[i]==0.0)
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result[i]=TailLog1(true,log_mode);
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else
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result[i]=TailLog0(true,log_mode);
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}
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return true;
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}
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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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if(x_arg<0)
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result[i]=TailLog0(true,log_mode);
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else
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{
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double pdf=p*MathPow(1.0-p,x_arg);
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result[i]=TailLogValue(pdf,true,log_mode);
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}
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Geometric mass function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability mass function of |
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//| the Geometric distribution with parameter p 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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//| p : Probability parameter |
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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 MathProbabilityDensityGeometric(const double &x[],const double p,double &result[])
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{
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return MathProbabilityDensityGeometric(x,p,false,result);
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}
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//+------------------------------------------------------------------+
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//| Geometric cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the cumulative distribution function of |
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//| the Geometric distribution with parameter p. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| p : Probability parameter |
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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 Geometric cumulative distribution function |
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//| with parameter p, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionGeometric(const double x,const double p,const bool tail,const bool log_mode,int &error_code)
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{
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//--- check NaN
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if(!MathIsValidNumber(x) || !MathIsValidNumber(p))
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{
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error_code=ERR_ARGUMENTS_NAN;
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return QNaN;
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}
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//--- check probability range
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if(p<=0.0 || p>1.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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error_code=ERR_OK;
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//--- check x
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if(x<0)
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return TailLog0(true,log_mode);
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//--- check p
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if(p==1.0)
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{
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if(x==0.0)
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return TailLog1(true,log_mode);
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else
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return TailLog0(true,log_mode);
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}
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//--- calculate cdf and take into account round-off errors for probability
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double cdf=1.0-MathPow(1.0-p,x+1.0);
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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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//| Geometric cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the cumulative distribution function of |
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//| the Geometric distribution with parameter p. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| p : Probability parameter |
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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 Geometric cumulative distribution function |
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//| with parameter p, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionGeometric(const double x,const double p,int &error_code)
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{
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return MathCumulativeDistributionGeometric(x,p,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Geometric 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 Geometric distribution with parameter p 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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//| p : Probability parameter |
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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 MathCumulativeDistributionGeometric(const double &x[],const double p,const bool tail,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(p))
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return false;
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//--- check probability range
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if(p<=0.0 || p>1.0)
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return false;
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int data_count=ArraySize(x);
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if(data_count==0)
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return false;
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int error_code=0;
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ArrayResize(result,data_count);
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//--- special case p==1.0
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if(p==1.0)
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{
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for(int i=0; i<data_count; i++)
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{
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if(x[i]==0.0)
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result[i]=TailLog1(true,log_mode);
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else
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result[i]=TailLog0(true,log_mode);
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}
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return true;
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}
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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)
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result[i]=TailLog0(true,log_mode);
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else
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result[i]=TailLogValue(MathMin(1.0-MathPow(1.0-p,x_arg+1.0),1.0),tail,log_mode);
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Geometric 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 Geometric distribution with parameter p 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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//| p : Probability parameter |
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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 MathCumulativeDistributionGeometric(const double &x[],const double p,double &result[])
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{
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return MathCumulativeDistributionGeometric(x,p,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Geometric distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the inverse cumulative distribution |
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//| function of Geometric distribution with parameter p for the |
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//| desired probability. |
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//| |
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//| Arguments: |
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//| probability : The desired probability |
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//| p : Probability parameter |
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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 Geometric inverse cumulative distribution |
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//| function with parameter p, evaluated at probability. |
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//+------------------------------------------------------------------+
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double MathQuantileGeometric(const double probability,const double p,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(p))
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{
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error_code=ERR_ARGUMENTS_NAN;
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return QNaN;
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}
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//--- check p range
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if(p<=0.0 || p>=1.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- calculate real probability
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double prob=TailLogProbability(probability,tail,log_mode);
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//--- check probability range
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if(prob<0.0 || prob>1.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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error_code=ERR_OK;
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//--- +infinity
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if(prob==1.0)
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return QPOSINF;
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if(prob==0.0)
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return 0.0;
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double res=MathCeil(-1.0+MathLog(1.0-prob)/MathLog(1.0-p)-1e-12);
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if(res<0)
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res=0;
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//--- return quantile
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return res;
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}
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//+------------------------------------------------------------------+
|
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//| Geometric distribution quantile function (inverse CDF) |
|
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//+------------------------------------------------------------------+
|
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//| The function returns the inverse cumulative distribution |
|
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//| function of the Geometric distribution with parameter p |
|
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//| for the desired probability. |
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//| |
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//| Arguments: |
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//| probability : The desired probability |
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//| p : Probability parameter |
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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 Geometric quantile function for probability. |
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//+------------------------------------------------------------------+
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double MathQuantileGeometric(const double probability,const double p,int &error_code)
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{
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return MathQuantileGeometric(probability,p,true,false,error_code);
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}
|
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//+------------------------------------------------------------------+
|
||||
//| Geometric distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates the inverse cumulative distribution |
|
||||
//| function of the Geometric distribution with parameter p |
|
||||
//| for values form the probability[] array. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| probability : Array with probabilities |
|
||||
//| p : Probability parameter |
|
||||
//| 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 MathQuantileGeometric(const double &probability[],const double p,const bool tail,const bool log_mode,double &result[])
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{
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//--- check parameters
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if(!MathIsValidNumber(p))
|
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return false;
|
||||
//--- check p range
|
||||
if(p<=0.0 || p>=1.0)
|
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return false;
|
||||
|
||||
int data_count=ArraySize(probability);
|
||||
if(data_count==0)
|
||||
return false;
|
||||
|
||||
int error_code=0;
|
||||
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)
|
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return false;
|
||||
|
||||
//--- +infinity
|
||||
if(prob==1.0)
|
||||
result[i]=QPOSINF;
|
||||
if(prob==0.0)
|
||||
result[i]=0.0;
|
||||
else
|
||||
{
|
||||
double res=MathCeil(-1.0+MathLog(1.0-prob)/MathLog(1.0-p)-1e-12);
|
||||
if(res<0)
|
||||
res=0;
|
||||
result[i]=res;
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Geometric distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates the inverse cumulative distribution |
|
||||
//| function of the Geometric distribution with parameter p |
|
||||
//| for values from the probability[] array. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| probability : Array with probabilities |
|
||||
//| p : Probability parameter |
|
||||
//| result : Array with calculated values |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if successful, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathQuantileGeometric(const double &probability[],const double p,double &result[])
|
||||
{
|
||||
return MathQuantileGeometric(probability,p,true,false,result);
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Geometric distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Computes the random variable from the Geometric distribution |
|
||||
//| with parameter p. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| p : Probability parameter |
|
||||
//| error_code : Variable for error code |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| The random value with Geometric distribution. |
|
||||
//+------------------------------------------------------------------+
|
||||
double MathRandomGeometric(const double p,int &error_code)
|
||||
{
|
||||
//--- check parameters
|
||||
if(!MathIsValidNumber(p))
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_NAN;
|
||||
return QNaN;
|
||||
}
|
||||
//--- check probability range
|
||||
if(p<0.0 || p>1.0)
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_INVALID;
|
||||
return QNaN;
|
||||
}
|
||||
|
||||
error_code=ERR_OK;
|
||||
//--- generate random number
|
||||
double rnd=MathRandomNonZero();
|
||||
double res=MathCeil(-1.0+MathLog(rnd)/MathLog(1.0-p)-1e-12);
|
||||
if(res<0)
|
||||
res=0;
|
||||
return res;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Geometric distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Generates random variables from the Geometric distribution with |
|
||||
//| parameter p. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| p : Probability parameter |
|
||||
//| data_count : Number of values needed |
|
||||
//| result : Output array with random values |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if successful, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathRandomGeometric(const double p,const int data_count,double &result[])
|
||||
{
|
||||
//--- check parameters
|
||||
if(!MathIsValidNumber(p))
|
||||
return false;
|
||||
//--- check probability range
|
||||
if(p<0.0 || p>1.0)
|
||||
return false;
|
||||
//--- prepare output array and calculate random values
|
||||
ArrayResize(result,data_count);
|
||||
for(int i=0; i<data_count; i++)
|
||||
{
|
||||
//--- generate random number
|
||||
double rnd=MathRandomNonZero();
|
||||
double res=MathCeil(-1.0+MathLog(rnd)/MathLog(1.0-p)-1e-12);
|
||||
if(res<0)
|
||||
res=0;
|
||||
result[i]=res;
|
||||
}
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Geometric distribution moments |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates 4 first moments of Geometric |
|
||||
//| distribution with parameter p. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| p : Probability parameter |
|
||||
//| 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 MathMomentsGeometric(const double p,double &mean,double &variance,double &skewness,double &kurtosis,int &error_code)
|
||||
{
|
||||
//--- default values
|
||||
mean =QNaN;
|
||||
variance=QNaN;
|
||||
skewness=QNaN;
|
||||
kurtosis=QNaN;
|
||||
//--- check NaN
|
||||
if(!MathIsValidNumber(p))
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_NAN;
|
||||
return false;
|
||||
}
|
||||
//--- check probability range
|
||||
if(p<=0.0 || p>=1.0)
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_INVALID;
|
||||
return(false);
|
||||
}
|
||||
|
||||
error_code=ERR_OK;
|
||||
//--- calculate moments
|
||||
mean =(1.0/p)-1;
|
||||
variance=(1.0-p)/(p*p);
|
||||
skewness=(2.0-p)/MathSqrt(1.0-p);
|
||||
kurtosis=(p*p-6*p+6)/(1-p);
|
||||
//--- successful
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
Reference in New Issue
Block a user