First commit [09/03/2018]
This commit is contained in:
Pierre8rTeam
@@ -0,0 +1,541 @@
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//+------------------------------------------------------------------+
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//| Uniform.mqh |
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//| Copyright 2016-2017, MetaQuotes Software Corp. |
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//| https://www.mql5.com |
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//+------------------------------------------------------------------+
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#property copyright "Copyright 2016-2017, MetaQuotes Software Corp."
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#property link "https://www.mql5.com"
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#include "Math.mqh"
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//+------------------------------------------------------------------+
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//| Uniform probability density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function of the |
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//| Uniform distribution with parameters a and b. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| a : Lower endpoint (minimum) |
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//| b : Upper endpoint (maximum) |
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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 density evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityUniform(const double x,const double a,const double b,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(a) || !MathIsValidNumber(b))
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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 range
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if(b<=a)
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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 ranges
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if(x>=a && x<=b)
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return TailLogValue(1.0/(b-a),true,log_mode);
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//--- otherwise 0
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return TailLog0(true,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Uniform probability density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function of the |
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//| Uniform distribution with parameters a and b. |
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| a : Lower endpoint (minimum) |
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//| b : Upper endpoint (maximum) |
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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 density evaluated at x. |
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//+------------------------------------------------------------------+
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double MathProbabilityDensityUniform(const double x,const double a,const double b,int &error_code)
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{
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return MathProbabilityDensityUniform(x,a,b,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Uniform probability density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of the |
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//| Uniform distribution with parameters a and b 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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//| a : Lower endpoint (minimum) |
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//| b : Upper endpoint (maximum) |
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//| log_mode : Logarithm mode flag, if true it returns Log values |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathProbabilityDensityUniform(const double &x[],const double a,const double b,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
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return false;
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//--- check range
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if(b<=a)
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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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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>=a && x_arg<=b)
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result[i]=TailLogValue(1.0/(b-a),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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//+------------------------------------------------------------------+
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//| Uniform probability density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of the |
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//| Uniform distribution with parameters a and b 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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//| mu : Mean |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathProbabilityDensityUniform(const double &x[],const double a,const double b,double &result[])
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{
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return MathProbabilityDensityUniform(x,a,b,false,result);
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}
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//+------------------------------------------------------------------+
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//| Uniform cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the cumulative distribution function |
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//| of the Uniform distribution with parameters a and b. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| a : Lower endpoint (minimum) |
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//| b : Upper endpoint (maximum) |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode flag,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 Uniform cumulative distribution function with |
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//| parameters a and b, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionUniform(const double x,const double a,const double b,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(x) || !MathIsValidNumber(a) || !MathIsValidNumber(b))
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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 ranges
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if(b<a)
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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>=a && x<=b)
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return TailLogValue(MathMin((x-a)/(b-a),1.0),tail,log_mode);
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if(x>b)
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return TailLog1(tail,log_mode);
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return TailLog0(tail,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Uniform 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 Uniform distribution with parameters a and b. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| a : Lower endpoint (minimum) |
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//| b : Upper endpoint (maximum) |
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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 Uniform cumulative distribution function with |
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//| parameters a and b, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionUniform(const double x,const double a,const double b,int &error_code)
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{
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return MathCumulativeDistributionUniform(x,a,b,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Uniform 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 Uniform distribution with parameters a and b 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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//| a : Mean |
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//| b : Scale |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode flag,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 MathCumulativeDistributionUniform(const double &x[],const double a,const double b,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(a) || !MathIsValidNumber(b))
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return false;
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//--- check ranges
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if(b<a)
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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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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>=a && x_arg<=b)
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result[i]=TailLogValue(MathMin((x_arg-a)/(b-a),1.0),tail,log_mode);
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else
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{
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if(x_arg>b)
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result[i]=TailLog1(tail,log_mode);
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else
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result[i]=TailLog0(tail,log_mode);
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}
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Uniform 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 Uniform distribution with parameters a and b 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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//| a : Mean |
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//| b : Scale |
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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 MathCumulativeDistributionUniform(const double &x[],const double a,const double b,double &result[])
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{
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return MathCumulativeDistributionUniform(x,a,b,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Uniform 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 Uniform distribution with parameters a and b |
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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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//| a : Lower endpoint (minimum) |
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//| b : Upper endpoint (maximum) |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode,if true it calculates for Log values|
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of the inverse cumulative distribution function |
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//| of Uniform distribution with parameters a and b. |
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//+------------------------------------------------------------------+
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double MathQuantileUniform(const double probability,const double a,const double b,const bool tail,const bool log_mode,int &error_code)
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{
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if(log_mode==true)
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{
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if(probability==QNEGINF)
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return 0.0;
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}
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//--- check parameters
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if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
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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 bounds
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if(b<a)
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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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if(b==a)
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return a;
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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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if(prob==0.0)
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return a;
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else
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if(prob==1.0)
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return b;
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//--- return quantile
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return a+prob*(b-a);
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}
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//+------------------------------------------------------------------+
|
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//| Uniform 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 Uniform distribution with parameters a and b |
|
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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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//| a : Lower endpoint (minimum) |
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//| b : Upper endpoint (maximum) |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of the inverse cumulative distribution function |
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//| of Uniform distribution with parameters a and b. |
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//+------------------------------------------------------------------+
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double MathQuantileUniform(const double probability,const double a,const double b,int &error_code)
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{
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return MathQuantileUniform(probability,a,b,true,false,error_code);
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}
|
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//+------------------------------------------------------------------+
|
||||
//| Uniform distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates the inverse cumulative distribution |
|
||||
//| function of Uniform distribution with parameters a and b |
|
||||
//| for values from the probability[] array. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| probability : Array with probabilities |
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//| a : Lower endpoint (minimum) |
|
||||
//| b : Upper endpoint (maximum) |
|
||||
//| tail : Flag to calculate lower tail |
|
||||
//| log_mode : Logarithm mode, if true it calculates Log values |
|
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//| result : Array with calculated values |
|
||||
//| |
|
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//| Return value: |
|
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//| true if successful, otherwise false. |
|
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//+------------------------------------------------------------------+
|
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bool MathQuantileUniform(const double &probability[],const double a,const double b,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(a) || !MathIsValidNumber(b))
|
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return false;
|
||||
//--- check ranges
|
||||
if(b<a)
|
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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;
|
||||
|
||||
int error_code=0;
|
||||
ArrayResize(result,data_count);
|
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for(int i=0; i<data_count; i++)
|
||||
{
|
||||
if(log_mode==true && probability[i]==QNEGINF)
|
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result[i]=0;
|
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else
|
||||
{
|
||||
//--- calculate real probability
|
||||
double prob=TailLogProbability(probability[i],tail,log_mode);
|
||||
//--- check probability range
|
||||
if(prob<0.0 || prob>1.0)
|
||||
return false;
|
||||
|
||||
//--- check bounds
|
||||
if(b==a)
|
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result[i]=a;
|
||||
else
|
||||
if(prob==0.0)
|
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result[i]=a;
|
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else
|
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if(prob==1.0)
|
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result[i]=b;
|
||||
else
|
||||
//--- quantile
|
||||
result[i]=(a+prob*(b-a));
|
||||
}
|
||||
}
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Uniform distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates the inverse cumulative distribution |
|
||||
//| function of Uniform distribution with parameters a and b |
|
||||
//| for values from the probability[] array. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| probability : Array with probabilities |
|
||||
//| a : Lower endpoint (minimum) |
|
||||
//| b : Upper endpoint (maximum) |
|
||||
//| result : Array with calculated values |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if successful, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathQuantileUniform(const double &probability[],const double a,const double b,double &result[])
|
||||
{
|
||||
return MathQuantileUniform(probability,a,b,true,false,result);
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Uniform distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Computes the random variable from the Uniform distribution |
|
||||
//| with parameters a and b. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| a : Lower endpoint (minimum) |
|
||||
//| b : Upper endpoint (maximum) |
|
||||
//| error_code : Variable for error code |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| The random value with uniform distribution. |
|
||||
//+------------------------------------------------------------------+
|
||||
double MathRandomUniform(const double a,const double b,int &error_code)
|
||||
{
|
||||
//--- check NaN
|
||||
if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_NAN;
|
||||
return QNaN;
|
||||
}
|
||||
//--- check upper bound
|
||||
if(b<a)
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_INVALID;
|
||||
return QNaN;
|
||||
}
|
||||
|
||||
error_code=ERR_OK;
|
||||
//--- check ranges
|
||||
if(a==b)
|
||||
return a;
|
||||
//---
|
||||
return a+MathRandomNonZero()*(b-a);
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Uniform distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Generates random variables from the Uniform distribution with |
|
||||
//| parameters a and b. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| a : Lower endpoint (minimum) |
|
||||
//| b : Upper endpoint (maximum) |
|
||||
//| data_count : Number of values needed |
|
||||
//| result : Output array with random values |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if successful, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathRandomUniform(const double a,const double b,const int data_count,double &result[])
|
||||
{
|
||||
//--- check NaN
|
||||
if(!MathIsValidNumber(a) || !MathIsValidNumber(b))
|
||||
return false;
|
||||
//--- check upper bound
|
||||
if(b<a)
|
||||
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();
|
||||
result[i]=a+rnd*(b-a);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Uniform distribution moments |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates 4 first moments of the Uniform |
|
||||
//| distribution with parameters a and b. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| a : Lower endpoint (minimum) |
|
||||
//| b : Upper endpoint (maximum) |
|
||||
//| 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 MathMomentsUniform(const double a,const double b,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(a) || !MathIsValidNumber(b))
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_NAN;
|
||||
return false;
|
||||
}
|
||||
//--- check range
|
||||
if(b<=a)
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_INVALID;
|
||||
return false;
|
||||
}
|
||||
|
||||
error_code=ERR_OK;
|
||||
//--- calculate moments
|
||||
mean =0.5*(a+b);
|
||||
variance=MathPow(b-a,2)/12;
|
||||
skewness=0;
|
||||
kurtosis=-3+9.0/5.0;
|
||||
//--- successful
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
Reference in New Issue
Block a user