567 lines
24 KiB
MQL5
567 lines
24 KiB
MQL5
 | //+------------------------------------------------------------------+
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//| Geometric.mqh |
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//| Copyright 2000-2025, MetaQuotes Ltd. |
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//| https://www.mql5.com |
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//+------------------------------------------------------------------+
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#include "Math.mqh"
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//+------------------------------------------------------------------+
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//| 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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//+------------------------------------------------------------------+
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//| Geometric distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the inverse cumulative distribution |
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//| function of the Geometric distribution with parameter p |
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//| for values form the probability[] array. |
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//| |
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//| Arguments: |
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//| probability : Array with probabilities |
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//| 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 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;
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//--- check p 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(probability);
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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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for(int i=0; i<data_count; i++)
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{
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//--- calculate real probability
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double prob=TailLogProbability(probability[i],tail,log_mode);
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//--- check probability range
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if(prob<0.0 || prob>1.0)
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return false;
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//--- +infinity
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if(prob==1.0)
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result[i]=QPOSINF;
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if(prob==0.0)
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result[i]=0.0;
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else
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{
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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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result[i]=res;
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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 distribution quantile function (inverse CDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the inverse cumulative distribution |
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//| function of the Geometric distribution with parameter p |
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//| 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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//| 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 MathQuantileGeometric(const double &probability[],const double p,double &result[])
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{
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return MathQuantileGeometric(probability,p,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Random variate from the Geometric distribution |
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//+------------------------------------------------------------------+
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//| Computes the random variable from the Geometric distribution |
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//| with parameter p. |
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//| |
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//| Arguments: |
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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 random value with Geometric distribution. |
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//+------------------------------------------------------------------+
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double MathRandomGeometric(const double p,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 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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//--- generate random number
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double rnd=MathRandomNonZero();
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double res=MathCeil(-1.0+MathLog(rnd)/MathLog(1.0-p)-1e-12);
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if(res<0)
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res=0;
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return res;
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}
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//+------------------------------------------------------------------+
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//| Random variate from the Geometric distribution |
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//+------------------------------------------------------------------+
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//| Generates random variables from the Geometric distribution with |
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//| parameter p. |
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//| |
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//| Arguments: |
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//| p : Probability parameter |
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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 MathRandomGeometric(const double p,const int data_count,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;
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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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//--- 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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{
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//--- generate random number
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double rnd=MathRandomNonZero();
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double res=MathCeil(-1.0+MathLog(rnd)/MathLog(1.0-p)-1e-12);
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if(res<0)
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res=0;
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result[i]=res;
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Geometric distribution moments |
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//+------------------------------------------------------------------+
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//| The function calculates 4 first moments of Geometric |
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//| distribution with parameter p. |
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//| |
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//| Arguments: |
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//| p : Probability parameter |
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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. |
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//+------------------------------------------------------------------+
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bool MathMomentsGeometric(const double p,double &mean,double &variance,double &skewness,double &kurtosis,int &error_code)
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{
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//--- 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;
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//--- check NaN
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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 false;
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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(false);
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}
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error_code=ERR_OK;
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//--- calculate moments
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mean =(1.0/p)-1;
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variance=(1.0-p)/(p*p);
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skewness=(2.0-p)/MathSqrt(1.0-p);
| |||
kurtosis=(p*p-6*p+6)/(1-p);
| |||
//--- successful
| |||
return true;
| |||
}
| |||
//+------------------------------------------------------------------+
|