531 行
24 KiB
MQL5
531 行
24 KiB
MQL5
 | //+------------------------------------------------------------------+
| ||
//| ChiSquare.mqh |
| |||
//| Copyright 2000-2025, MetaQuotes Ltd. |
| |||
//| https://www.mql5.com |
| |||
//+------------------------------------------------------------------+
| |||
#include "Math.mqh"
| |||
#include "Gamma.mqh"
| |||
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square density function (PDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function returns the probability density function |
| |||
//| of the Chi-Square distribution with parameter nu. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| x : Random variable |
| |||
//| nu : Degrees of freedom |
| |||
//| log_mode : Logarithm mode flag, if true it returns Log values |
| |||
//| error_code : Variable for error code |
| |||
//| |
| |||
//| Return value: |
| |||
//| The probability density evaluated at x. |
| |||
//+------------------------------------------------------------------+
| |||
double MathProbabilityDensityChiSquare(const double x,const double nu,const bool log_mode,int &error_code)
| |||
{
| |||
//--- check arguments
| |||
if(!MathIsValidNumber(x) || !MathIsValidNumber(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_NAN;
| |||
return QNaN;
| |||
}
| |||
//--- nu must be positive integer
| |||
if(nu<=0 || nu!=MathRound(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_INVALID;
| |||
return QNaN;
| |||
}
| |||
| |||
error_code=ERR_OK;
| |||
if(x<=0.0)
| |||
return TailLog0(true,log_mode);
| |||
| |||
//--- calculate using Gamma density
| |||
double pdf=MathProbabilityDensityGamma(x,nu*0.5,2.0,error_code);
| |||
if(log_mode==true)
| |||
return MathLog(pdf);
| |||
return pdf;
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square density function (PDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function returns the probability density function |
| |||
//| of the Chi-Square distribution with parameter nu. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| x : Random variable |
| |||
//| nu : Degrees of freedom |
| |||
//| error_code : Variable for error code |
| |||
//| |
| |||
//| Return value: |
| |||
//| The probability density evaluated at x. |
| |||
//+------------------------------------------------------------------+
| |||
double MathProbabilityDensityChiSquare(const double x,const double nu,int &error_code)
| |||
{
| |||
return MathProbabilityDensityChiSquare(x,nu,false,error_code);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square density function (PDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function calculates the probability density function of the |
| |||
//| ChiSquare distribution with parameter nu for values in x[] array.|
| |||
//| |
| |||
//| Arguments: |
| |||
//| x : Array with random variables |
| |||
//| nu : Degrees of freedom |
| |||
//| log_mode : Logarithm mode flag, if true it returns Log values |
| |||
//| result : Array with calculated values |
| |||
//| |
| |||
//| Return value: |
| |||
//| true if successful, otherwise false. |
| |||
//+------------------------------------------------------------------+
| |||
bool MathProbabilityDensityChiSquare(const double &x[],const double nu,const bool log_mode,double &result[])
| |||
{
| |||
//--- check arguments
| |||
if(!MathIsValidNumber(nu))
| |||
return false;
| |||
//--- nu must be positive integer
| |||
if(nu<=0 || nu!=MathRound(nu))
| |||
return false;
| |||
| |||
int data_count=ArraySize(x);
| |||
if(data_count==0)
| |||
return false;
| |||
| |||
int error_code=0;
| |||
ArrayResize(result,data_count);
| |||
for(int i=0; i<data_count; i++)
| |||
{
| |||
double x_arg=x[i];
| |||
| |||
if(!MathIsValidNumber(x_arg))
| |||
return false;
| |||
| |||
if(x_arg<=0.0)
| |||
result[i]=TailLog0(true,log_mode);
| |||
else
| |||
{
| |||
//--- calculate using Gamma density
| |||
double pdf=MathProbabilityDensityGamma(x_arg,nu*0.5,2.0,error_code);
| |||
if(log_mode==true)
| |||
result[i]=MathLog(pdf);
| |||
else
| |||
result[i]=pdf;
| |||
}
| |||
}
| |||
return true;
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square density function (PDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function calculates the probability density function of the |
| |||
//| ChiSquare distribution with parameter nu for values in x[] array.|
| |||
//| |
| |||
//| Arguments: |
| |||
//| x : Array with random variables |
| |||
//| nu : Degrees of freedom |
| |||
//| result : Array with calculated values |
| |||
//| |
| |||
//| Return value: |
| |||
//| true if successful, otherwise false. |
| |||
//+------------------------------------------------------------------+
| |||
bool MathProbabilityDensityChiSquare(const double &x[],const double nu,double &result[])
| |||
{
| |||
return MathProbabilityDensityChiSquare(x,nu,false,result);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square cumulative distribution function (CDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function returns the cumulative distribution function of the |
| |||
//| Chi-Square distribution with given nu, evaluated at x. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| x : The desired quantile |
| |||
//| nu : Degrees of freedom |
| |||
//| 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 Chi-Square cumulative distribution function with |
| |||
//| parameter nu, evaluated at x. |
| |||
//+------------------------------------------------------------------+
| |||
double MathCumulativeDistributionChiSquare(const double x,const double nu,const bool tail,const bool log_mode,int &error_code)
| |||
{
| |||
//--- check x
| |||
if(!MathIsValidNumber(x) || !MathIsValidNumber(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_NAN;
| |||
return QNaN;
| |||
}
| |||
//--- nu must be positive integer
| |||
if(nu<=0 || nu!=MathRound(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_INVALID;
| |||
return QNaN;
| |||
}
| |||
| |||
error_code=ERR_OK;
| |||
if(x<=0.0)
| |||
return TailLog0(true,log_mode);
| |||
//---- calculate using Gamma distribution
| |||
return MathCumulativeDistributionGamma(x,nu*0.5,2.0,tail,log_mode,error_code);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square cumulative distribution function (CDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function returns the cumulative distribution function of the |
| |||
//| Chi-Square distribution with given nu, evaluated at x. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| x : The desired quantile |
| |||
//| nu : Degrees of freedom |
| |||
//| error_code : Variable for error code |
| |||
//| |
| |||
//| Return value: |
| |||
//| The value of Chi-Square cumulative distribution function with |
| |||
//| parameter nu, evaluated at x. |
| |||
//+------------------------------------------------------------------+
| |||
double MathCumulativeDistributionChiSquare(const double x,const double nu,int &error_code)
| |||
{
| |||
return MathCumulativeDistributionChiSquare(x,nu,true,false,error_code);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square cumulative distribution function (CDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function calculates the cumulative distribution function of |
| |||
//| the Chi-Square distribution with parameter nu for values in x[]. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| x : Array with random variables |
| |||
//| nu : Degrees of freedom |
| |||
//| 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 MathCumulativeDistributionChiSquare(const double &x[],const double nu,const bool tail,const bool log_mode,double &result[])
| |||
{
| |||
//--- check NaN
| |||
if(!MathIsValidNumber(nu))
| |||
return false;
| |||
//--- nu must be positive integer
| |||
if(nu<=0 || nu!=MathRound(nu))
| |||
return false;
| |||
| |||
int data_count=ArraySize(x);
| |||
if(data_count==0)
| |||
return false;
| |||
| |||
int error_code=0;
| |||
ArrayResize(result,data_count);
| |||
for(int i=0; i<data_count; i++)
| |||
{
| |||
double x_arg=x[i];
| |||
| |||
if(!MathIsValidNumber(x_arg))
| |||
return false;
| |||
| |||
if(x_arg<=0.0)
| |||
result[i]=TailLog0(true,log_mode);
| |||
else
| |||
{
| |||
double cdf=MathCumulativeDistributionGamma(x_arg,nu*0.5,2.0,true,false,error_code);
| |||
result[i]=TailLogValue(cdf,tail,log_mode);
| |||
}
| |||
}
| |||
return true;
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square cumulative distribution function (CDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function calculates the cumulative distribution function of |
| |||
//| the Chi-Square distribution with parameter nu for values in x[]. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| x : Array with random variables |
| |||
//| nu : Degrees of freedom |
| |||
//| result : Array with calculated values |
| |||
//| |
| |||
//| Return value: |
| |||
//| true if successful, otherwise false. |
| |||
//+------------------------------------------------------------------+
| |||
bool MathCumulativeDistributionChiSquare(const double &x[],const double nu,double &result[])
| |||
{
| |||
return MathCumulativeDistributionChiSquare(x,nu,true,false,result);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square distribution quantile function (inverse CDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function returns the inverse cumulative distribution |
| |||
//| function of the Chi-Square distribution with parameter nu |
| |||
//| for the desired probability. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| probability : The desired probability |
| |||
//| nu : Degrees of freedom |
| |||
//| 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 inverse cumulative distribution function |
| |||
//| of the Chi-Square distribution with parameter nu. |
| |||
//+------------------------------------------------------------------+
| |||
double MathQuantileChiSquare(const double probability,const double nu,const bool tail,const bool log_mode,int &error_code)
| |||
{
| |||
//--- check NaN
| |||
if(!MathIsValidNumber(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_NAN;
| |||
return QNaN;
| |||
}
| |||
//--- nu must be positive
| |||
if(nu<=0)
| |||
{
| |||
error_code=ERR_ARGUMENTS_INVALID;
| |||
return QNaN;
| |||
}
| |||
//--- nu must be integer
| |||
if(nu!=MathRound(nu))
| |||
{
| |||
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;
| |||
if(prob==0.0)
| |||
return 0.0;
| |||
| |||
if(prob==1.0)
| |||
return QPOSINF;
| |||
| |||
//---- calculate quantile using Gamma distribution
| |||
return MathQuantileGamma(prob,nu*0.5,2.0,error_code);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square distribution quantile function (inverse CDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function returns the inverse cumulative distribution |
| |||
//| function of the Chi-Square distribution with parameter nu |
| |||
//| for the desired probability. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| probability : The desired probability |
| |||
//| nu : Degrees of freedom |
| |||
//| error_code : Variable for error code |
| |||
//| |
| |||
//| Return value: |
| |||
//| The value of the inverse cumulative distribution function |
| |||
//| of the Chi-Square distribution with parameter nu. |
| |||
//+------------------------------------------------------------------+
| |||
double MathQuantileChiSquare(const double probability,const double nu,int &error_code)
| |||
{
| |||
return MathQuantileChiSquare(probability,nu,true,false,error_code);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square distribution quantile function (inverse CDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function calculates the inverse cumulative distribution |
| |||
//| function of the Chi-Square distribution with parameter nu |
| |||
//| for values from the probability[] array. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| probability : Array with probabilities |
| |||
//| nu : Degrees of freedom |
| |||
//| 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 MathQuantileChiSquare(const double &probability[],const double nu,const bool tail,const bool log_mode,double &result[])
| |||
{
| |||
//--- check NaN
| |||
if(!MathIsValidNumber(nu))
| |||
return false;
| |||
//--- nu must be positive
| |||
if(nu<=0)
| |||
return false;
| |||
//--- nu must be integer
| |||
if(nu!=MathRound(nu))
| |||
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;
| |||
| |||
if(prob==0.0)
| |||
result[i]=0.0;
| |||
else
| |||
if(prob==1.0)
| |||
result[i]=QPOSINF;
| |||
else
| |||
{
| |||
//--- calculate using Gamma distribution
| |||
result[i]=MathQuantileGamma(prob,nu*0.5,2.0,error_code);
| |||
}
| |||
}
| |||
return true;
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square distribution quantile function (inverse CDF) |
| |||
//+------------------------------------------------------------------+
| |||
//| The function calculates the inverse cumulative distribution |
| |||
//| function of the Chi-Square distribution with parameter nu |
| |||
//| for values from the probability[] array. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| probability : Array with probabilities |
| |||
//| nu : Degrees of freedom |
| |||
//| result : Array with calculated values |
| |||
//| |
| |||
//| Return value: |
| |||
//| true if successful, otherwise false. |
| |||
//+------------------------------------------------------------------+
| |||
bool MathQuantileChiSquare(const double &probability[],const double nu,double &result[])
| |||
{
| |||
return MathQuantileChiSquare(probability,nu,true,false,result);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Random variate from the Chi-Square distribution |
| |||
//+------------------------------------------------------------------+
| |||
//| Computes the random variable from the Chi-Square distribution |
| |||
//| with parameter nu. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| nu : Degrees of freedom |
| |||
//| error_code : Variable for error code |
| |||
//| |
| |||
//| Return value: |
| |||
//| The random value with Chi-Square distribution. |
| |||
//+------------------------------------------------------------------+
| |||
double MathRandomChiSquare(const double nu,int &error_code)
| |||
{
| |||
//--- NaN
| |||
if(!MathIsValidNumber(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_NAN;
| |||
return QNaN;
| |||
}
| |||
//--- nu must be integer
| |||
if(nu!=MathRound(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_INVALID;
| |||
return QNaN;
| |||
}
| |||
//--- nu must be positive
| |||
if(nu<=0)
| |||
{
| |||
error_code=ERR_ARGUMENTS_INVALID;
| |||
return QNaN;
| |||
}
| |||
| |||
error_code=ERR_OK;
| |||
//--- return gamma(nu/2,2)
| |||
return MathRandomGamma(nu*0.5,2.0,error_code);
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Random variate from Chi-Square distribution |
| |||
//+------------------------------------------------------------------+
| |||
//| Generates random variables from the Chi-Square distribution |
| |||
//| with parameter nu. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| nu : Degrees of freedom |
| |||
//| data_count : Number of values needed |
| |||
//| result : Output array with random values |
| |||
//| |
| |||
//| Return value: |
| |||
//| true if successful, otherwise false. |
| |||
//+------------------------------------------------------------------+
| |||
bool MathRandomChiSquare(const double nu,const int data_count,double &result[])
| |||
{
| |||
//--- check NaN
| |||
if(!MathIsValidNumber(nu))
| |||
return false;
| |||
//--- nu must be integer
| |||
if(nu!=MathRound(nu))
| |||
return false;
| |||
//--- nu must be positive
| |||
if(nu<=0)
| |||
return false;
| |||
int error_code=0;
| |||
//--- prepare output array and calculate random values
| |||
ArrayResize(result,data_count);
| |||
for(int i=0; i<data_count; i++)
| |||
{
| |||
//--- generate Gamma random number
| |||
result[i]=MathRandomGamma(nu*0.5,2.0,error_code);
| |||
}
| |||
return true;
| |||
}
| |||
//+------------------------------------------------------------------+
| |||
//| Chi-Square distribution moments |
| |||
//+------------------------------------------------------------------+
| |||
//| The function calculates 4 first moments of Chi-Square |
| |||
//| distribution with parameter nu. |
| |||
//| |
| |||
//| Arguments: |
| |||
//| nu : Degrees of freedom |
| |||
//| 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 MathMomentsChiSquare(const double nu,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(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_NAN;
| |||
return false;
| |||
}
| |||
//--- nu must be positive integer
| |||
if(nu<=0 || nu!=MathRound(nu))
| |||
{
| |||
error_code=ERR_ARGUMENTS_INVALID;
| |||
return false;
| |||
}
| |||
| |||
error_code=ERR_OK;
| |||
//--- calculate moments
| |||
mean =nu;
| |||
variance=2*nu;
| |||
skewness=MathSqrt(8/nu);
| |||
kurtosis=12/nu;
| |||
//--- successful
| |||
return true;
| |||
}
| |||
//+------------------------------------------------------------------+
|