| //+------------------------------------------------------------------+
|
| //| Geometric.mqh |
|
| //| Copyright 2000-2025, MetaQuotes Ltd. |
|
| //| https://www.mql5.com |
|
| //+------------------------------------------------------------------+
|
| #include "Math.mqh"
|
|
|
| //+------------------------------------------------------------------+
|
| //| Geometric mass function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability mass function of the |
|
| //| Geometric distribution with parameter p. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Random variable |
|
| //| p : Probability parameter |
|
| //| log_mode : Logarithm mode flag, if true it returns Log values |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The probability mass evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathProbabilityDensityGeometric(const double x,const double p,const bool log_mode,int &error_code)
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(x) || !MathIsValidNumber(p))
|
| {
|
| error_code=ERR_ARGUMENTS_NAN;
|
| return QNaN;
|
| }
|
| //--- check probability
|
| if(p<=0.0 || p>1.0)
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
| //--- check x
|
| if(x!=MathRound(x))
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
|
|
| error_code=ERR_OK;
|
| if(x<0)
|
| return TailLog0(true,log_mode);
|
|
|
| if(p==1.0)
|
| {
|
| if(x==0.0)
|
| return TailLog1(true,log_mode);
|
| else
|
| return TailLog0(true,log_mode);
|
| }
|
| //--- return geometric density
|
| return TailLogValue(p*MathPow(1.0-p,x),true,log_mode);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric mass function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the probability mass function of |
|
| //| the Geometric distribution with parameter p. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Random variable |
|
| //| p : Probability parameter |
|
| //| log_mode : Logarithm mode flag, if true it returns Log values |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The probability mass evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathProbabilityDensityGeometric(const double x,const double p,int &error_code)
|
| {
|
| return MathProbabilityDensityGeometric(x,p,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric mass function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the probability mass function of |
|
| //| the Geometric distribution with parameter p for values in x[]. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| p : Probability parameter |
|
| //| log_mode : Logarithm mode, if true it calculates Log values |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathProbabilityDensityGeometric(const double &x[],const double p,const bool log_mode,double &result[])
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(p))
|
| return false;
|
| //--- check probability
|
| if(p<=0.0 || p>1.0)
|
| return false;
|
|
|
| int data_count=ArraySize(x);
|
| if(data_count==0)
|
| return false;
|
|
|
| int error_code=0;
|
| ArrayResize(result,data_count);
|
|
|
| //--- special case p==1.0
|
| if(p==1.0)
|
| {
|
| for(int i=0; i<data_count; i++)
|
| {
|
| if(x[i]==0.0)
|
| result[i]=TailLog1(true,log_mode);
|
| else
|
| result[i]=TailLog0(true,log_mode);
|
| }
|
| return true;
|
| }
|
|
|
| for(int i=0; i<data_count; i++)
|
| {
|
| double x_arg=x[i];
|
|
|
| if(!MathIsValidNumber(x_arg))
|
| return false;
|
|
|
| if(x_arg!=MathRound(x_arg))
|
| return false;
|
|
|
| if(x_arg<0)
|
| result[i]=TailLog0(true,log_mode);
|
| else
|
| {
|
| double pdf=p*MathPow(1.0-p,x_arg);
|
| result[i]=TailLogValue(pdf,true,log_mode);
|
| }
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric mass function (PDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the probability mass function of |
|
| //| the Geometric distribution with parameter p for values in x[]. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| p : Probability parameter |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathProbabilityDensityGeometric(const double &x[],const double p,double &result[])
|
| {
|
| return MathProbabilityDensityGeometric(x,p,false,result);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the cumulative distribution function of |
|
| //| the Geometric distribution with parameter p. |
|
| //| |
|
| //| Arguments: |
|
| //| x : The desired quantile |
|
| //| p : Probability parameter |
|
| //| tail : Flag to calculate lower tail |
|
| //| log_mode : Logarithm mode,if true it calculates Log values |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The value of the Geometric cumulative distribution function |
|
| //| with parameter p, evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathCumulativeDistributionGeometric(const double x,const double p,const bool tail,const bool log_mode,int &error_code)
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(x) || !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;
|
| //--- check x
|
| if(x<0)
|
| return TailLog0(true,log_mode);
|
| //--- check p
|
| if(p==1.0)
|
| {
|
| if(x==0.0)
|
| return TailLog1(true,log_mode);
|
| else
|
| return TailLog0(true,log_mode);
|
| }
|
| //--- calculate cdf and take into account round-off errors for probability
|
| double cdf=1.0-MathPow(1.0-p,x+1.0);
|
| return TailLogValue(MathMin(cdf,1.0),tail,log_mode);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the cumulative distribution function of |
|
| //| the Geometric distribution with parameter p. |
|
| //| |
|
| //| Arguments: |
|
| //| x : The desired quantile |
|
| //| p : Probability parameter |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The value of the Geometric cumulative distribution function |
|
| //| with parameter p, evaluated at x. |
|
| //+------------------------------------------------------------------+
|
| double MathCumulativeDistributionGeometric(const double x,const double p,int &error_code)
|
| {
|
| return MathCumulativeDistributionGeometric(x,p,true,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the cumulative distribution function of |
|
| //| the Geometric distribution with parameter p for values in x[]. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| 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. |
|
| //+------------------------------------------------------------------+
|
| bool MathCumulativeDistributionGeometric(const double &x[],const double p,const bool tail,const bool log_mode,double &result[])
|
| {
|
| //--- check NaN
|
| if(!MathIsValidNumber(p))
|
| return false;
|
| //--- check probability range
|
| if(p<=0.0 || p>1.0)
|
| return false;
|
|
|
| int data_count=ArraySize(x);
|
| if(data_count==0)
|
| return false;
|
|
|
| int error_code=0;
|
| ArrayResize(result,data_count);
|
|
|
| //--- special case p==1.0
|
| if(p==1.0)
|
| {
|
| for(int i=0; i<data_count; i++)
|
| {
|
| if(x[i]==0.0)
|
| result[i]=TailLog1(true,log_mode);
|
| else
|
| result[i]=TailLog0(true,log_mode);
|
| }
|
| return true;
|
| }
|
|
|
| for(int i=0; i<data_count; i++)
|
| {
|
| double x_arg=x[i];
|
|
|
| if(!MathIsValidNumber(x_arg))
|
| return false;
|
|
|
| if(x_arg<0)
|
| result[i]=TailLog0(true,log_mode);
|
| else
|
| result[i]=TailLogValue(MathMin(1.0-MathPow(1.0-p,x_arg+1.0),1.0),tail,log_mode);
|
| }
|
| return true;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric cumulative distribution function (CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function calculates the cumulative distribution function of |
|
| //| the Geometric distribution with parameter p for values in x[]. |
|
| //| |
|
| //| Arguments: |
|
| //| x : Array with random variables |
|
| //| p : Probability parameter |
|
| //| result : Array with calculated values |
|
| //| |
|
| //| Return value: |
|
| //| true if successful, otherwise false. |
|
| //+------------------------------------------------------------------+
|
| bool MathCumulativeDistributionGeometric(const double &x[],const double p,double &result[])
|
| {
|
| return MathCumulativeDistributionGeometric(x,p,true,false,result);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric distribution quantile function (inverse CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the inverse cumulative distribution |
|
| //| function of Geometric distribution with parameter p for the |
|
| //| desired probability. |
|
| //| |
|
| //| Arguments: |
|
| //| probability : The desired probability |
|
| //| p : Probability parameter |
|
| //| tail : Flag to calculate lower tail |
|
| //| log_mode : Logarithm mode,if true it calculates for Log values|
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The value of the Geometric inverse cumulative distribution |
|
| //| function with parameter p, evaluated at probability. |
|
| //+------------------------------------------------------------------+
|
| double MathQuantileGeometric(const double probability,const double p,const bool tail,const bool log_mode,int &error_code)
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(p))
|
| {
|
| error_code=ERR_ARGUMENTS_NAN;
|
| return QNaN;
|
| }
|
| //--- check p range
|
| if(p<=0.0 || p>=1.0)
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
|
|
| //--- calculate real probability
|
| double prob=TailLogProbability(probability,tail,log_mode);
|
| //--- check probability range
|
| if(prob<0.0 || prob>1.0)
|
| {
|
| error_code=ERR_ARGUMENTS_INVALID;
|
| return QNaN;
|
| }
|
|
|
| error_code=ERR_OK;
|
| //--- +infinity
|
| if(prob==1.0)
|
| return QPOSINF;
|
| if(prob==0.0)
|
| return 0.0;
|
|
|
| double res=MathCeil(-1.0+MathLog(1.0-prob)/MathLog(1.0-p)-1e-12);
|
| if(res<0)
|
| res=0;
|
| //--- return quantile
|
| return res;
|
| }
|
| //+------------------------------------------------------------------+
|
| //| Geometric distribution quantile function (inverse CDF) |
|
| //+------------------------------------------------------------------+
|
| //| The function returns the inverse cumulative distribution |
|
| //| function of the Geometric distribution with parameter p |
|
| //| for the desired probability. |
|
| //| |
|
| //| Arguments: |
|
| //| probability : The desired probability |
|
| //| p : Probability parameter |
|
| //| error_code : Variable for error code |
|
| //| |
|
| //| Return value: |
|
| //| The value of the Geometric quantile function for probability. |
|
| //+------------------------------------------------------------------+
|
| double MathQuantileGeometric(const double probability,const double p,int &error_code)
|
| {
|
| return MathQuantileGeometric(probability,p,true,false,error_code);
|
| }
|
| //+------------------------------------------------------------------+
|
| //| 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. |
|
| //+------------------------------------------------------------------+
|
| bool MathQuantileGeometric(const double &probability[],const double p,const bool tail,const bool log_mode,double &result[])
|
| {
|
| //--- check parameters
|
| if(!MathIsValidNumber(p))
|
| return false;
|
| //--- check p range
|
| if(p<=0.0 || p>=1.0)
|
| 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)
|
| 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;
|
| }
|
| //+------------------------------------------------------------------+
|
