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mql5/Include/Math/Stat/NoncentralChiSquare.mqh

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MQL5
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2025-08-05 01:57:33 -04:00
//+------------------------------------------------------------------+
//| NoncentralChiSquare.mqh |
//| Copyright 2000-2025, MetaQuotes Ltd. |
//| https://www.mql5.com |
//+------------------------------------------------------------------+
#include "Math.mqh"
#include "Normal.mqh"
#include "Poisson.mqh"
#include "ChiSquare.mqh"
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution density function (PDF) |
//+------------------------------------------------------------------+
//| The function returns the probability density function of the |
//| Noncentral Chi-Square distribution with parameters nu and sigma. |
//| |
//| Arguments: |
//| x : Random variable |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| 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 MathProbabilityDensityNoncentralChiSquare(const double x,const double nu,const double sigma,const bool log_mode,int &error_code)
{
//--- check NaN
if(!MathIsValidNumber(x) || !MathIsValidNumber(nu) || !MathIsValidNumber(sigma))
{
error_code=ERR_ARGUMENTS_NAN;
return QNaN;
}
//--- check arguments
if(nu!=MathRound(nu) || nu<=0.0)
{
error_code=ERR_ARGUMENTS_INVALID;
return QNaN;
}
error_code=ERR_OK;
if(x<=0.0)
return TailLog0(true,log_mode);
//--- prepare parameters
int err_code=0;
int max_terms=1000;
double lambda=sigma*0.5;
double half_nu=nu*0.5;
double pwr_lambda=1.0;
double pwr_two=MathExp(-half_nu*MathLog(2));
double pwr_x=MathExp((half_nu-1.0)*MathLog(x));
double fact_mult=1.0;
double coef_lambda_x=MathExp(-lambda-x*0.5);
double coef_gamma=1.0/MathGamma(half_nu);
double inv_factor=1.0;
//--- calculate density using direct summation
int j=0;
double pdf=0;
while(j<max_terms)
{
if(j>0)
{
pwr_lambda*=lambda;
pwr_x*=x;
pwr_two*=0.5;
fact_mult*=1.0/j;
inv_factor*=1.0/(j+half_nu-1);
}
double dp=coef_gamma*inv_factor*pwr_lambda*pwr_two*pwr_x*fact_mult*coef_lambda_x;
pdf=pdf+dp;
//--- check stop
if(dp/(pdf+10E-10)<10E-16)
break;
j++;
}
//--- check convergence
if(j<max_terms)
return TailLogValue(pdf,true,log_mode);
else
{
error_code=ERR_NON_CONVERGENCE;
return QNaN;
}
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution density function (PDF) |
//+------------------------------------------------------------------+
//| The function returns the probability density function of the |
//| Noncentral Chi-Square distribution with parameters nu and sigma. |
//| |
//| Arguments: |
//| x : Random variable |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| error_code : Variable for error code |
//| |
//| Return value: |
//| The probability density evaluated at x. |
//+------------------------------------------------------------------+
double MathProbabilityDensityNoncentralChiSquare(double x,const double nu,const double sigma,int &error_code)
{
return MathProbabilityDensityNoncentralChiSquare(x,nu,sigma,false,error_code);
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution density function (PDF) |
//+------------------------------------------------------------------+
//| The function calculates the probability density function of |
//| the Chi Square distribution with parameter nu for values in x. |
//| |
//| Arguments: |
//| x : Array with random variables |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| log_mode : Logarithm mode flag, if true it returns Log values |
//| result : Array with calculated values |
//| |
//| Return value: |
//| true if successful, otherwise false. |
//+------------------------------------------------------------------+
bool MathProbabilityDensityNoncentralChiSquare(const double &x[],const double nu,const double sigma,const bool log_mode,double &result[])
{
//--- check NaN
if(!MathIsValidNumber(nu) || !MathIsValidNumber(sigma))
return false;
//--- check arguments
if(nu!=MathRound(nu) || nu<=0.0)
return false;
int data_count=ArraySize(x);
if(data_count==0)
return false;
ArrayResize(result,data_count);
//--- prepare parameters
int max_terms=1000;
double lambda=sigma*0.5;
double half_nu=nu*0.5;
double coef_gamma=1.0/MathGamma(half_nu);
double pwr_two2=MathExp(-half_nu*MathLog(2));
double pwr_half_num1=(half_nu-1.0);
double coef_exp_lambda=MathExp(-lambda);
for(int i=0; i<data_count; i++)
{
double x_arg=x[i];
if(x_arg<=0)
result[i]=TailLog0(true,log_mode);
else
{
int err_code=0;
//result[i]=MathProbabilityDensityNoncentralChiSquare(x_arg,nu,sigma,false,err_code);
double pwr_lambda=1.0;
double pwr_two=pwr_two2;
double pwr_x=MathPow(x_arg,pwr_half_num1);
double fact_mult=1.0;
double coef_lambda_x=coef_exp_lambda*MathExp(-x_arg*0.5);
double inv_factor=1.0;
//--- calculate density using direct summation
int j=0;
double pdf=0;
while(j<max_terms)
{
if(j>0)
{
pwr_lambda*=lambda;
pwr_x*=x_arg;
pwr_two*=0.5;
fact_mult*=1.0/j;
inv_factor*=1.0/(j+half_nu-1);
}
double dp=coef_gamma*inv_factor*pwr_lambda*pwr_two*pwr_x*fact_mult*coef_lambda_x;
pdf=pdf+dp;
//--- check stop
if(dp/(pdf+10E-10)<10E-16)
break;
j++;
}
//--- check convergence
if(j<max_terms)
result[i]=TailLogValue(pdf,true,log_mode);
else
return false;
}
}
return true;
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution density function (PDF) |
//+------------------------------------------------------------------+
//| The function calculates the probability density function of |
//| the Chi-Square distribution with parameter nu for values in x[]. |
//| |
//| Arguments: |
//| x : Array with random variables |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| result : Array with calculated values |
//| |
//| Return value: |
//| true if successful, otherwise false. |
//+------------------------------------------------------------------+
bool MathProbabilityDensityNoncentralChiSquare(const double &x[],const double nu,const double sigma,double &result[])
{
return MathProbabilityDensityNoncentralChiSquare(x,nu,sigma,false,result);
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square cumulative distribution function (CDF) |
//+------------------------------------------------------------------+
//| The function returns the probability that an observation |
//| from a Noncentral Chi-Square distribution with parameters |
//| nu and sigma is less than or equal to x. |
//| |
//| Arguments: |
//| x : The desired quantile |
//| nu : Degrees of freedom |
//| sigma : Noncentrality 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 Noncentral Chi-Square cumulative distribution |
//| function with parameters nu and sigma, evaluated at x. |
//+------------------------------------------------------------------+
double MathCumulativeDistributionNoncentralChiSquare(const double x,const double nu,const double sigma,const bool tail,const bool log_mode,int &error_code)
{
//--- check NaN
if(!MathIsValidNumber(x) || !MathIsValidNumber(nu) || !MathIsValidNumber(sigma))
{
error_code=ERR_ARGUMENTS_NAN;
return QNaN;
}
//--- check arguments
if(nu!=MathRound(nu) || nu<=0.0)
{
error_code=ERR_ARGUMENTS_INVALID;
return QNaN;
}
error_code=ERR_OK;
if(x<=0.0)
return TailLog0(true,log_mode);
//--- prepare parameters
double cdf=0.0;
int max_terms=100;
double lambda=sigma*0.5;
double coef_lambda=MathExp(-lambda);
double pwr_lambda=1.0;
double fact_mult=1.0;
double half_x=x*0.5;
double half_nu=nu*0.5;
//--- direct summation
int j=0;
while(j<max_terms)
{
if(j>0)
{
pwr_lambda*=lambda;
fact_mult/=j;
}
double coef1=coef_lambda*pwr_lambda*fact_mult;
double coef2=MathMin(MathGammaIncomplete(half_x,half_nu+j),1.0);
double dp=coef1*coef2;
cdf=cdf+dp;
if((dp/(cdf+10E-10))<10E-16)
break;
j++;
}
//---
if(j<max_terms)
{
//--- take into account round-off errors for probability
cdf=MathMin(cdf,1.0);
return TailLogValue(cdf,tail,log_mode);
}
else
{
error_code=ERR_NON_CONVERGENCE;
return QNaN;
}
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square cumulative distribution function (CDF) |
//+------------------------------------------------------------------+
//| The function returns the probability that an observation |
//| from a Noncentral Chi-Square distribution with parameters |
//| nu and sigma is less than or equal to x. |
//| |
//| Arguments: |
//| x : The desired quantile |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| error_code : Variable for error code |
//| |
//| Return value: |
//| The value of Noncentral Chi-Square cumulative distribution |
//| function with parameters nu and sigma, evaluated at x. |
//+------------------------------------------------------------------+
double MathCumulativeDistributionNoncentralChiSquare(const double x,const double nu,const double sigma,int &error_code)
{
return MathCumulativeDistributionNoncentralChiSquare(x,nu,sigma,true,false,error_code);
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square cumulative distribution function (CDF) |
//+------------------------------------------------------------------+
//| The function calculates the cumulative distribution function of |
//| the Noncentral Chi-Square distribution with parameters nu and |
//| sigma for values in x. |
//| |
//| Arguments: |
//| x : Array with random variables |
//| nu : Degrees of freedom |
//| sigma : Noncentrality 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 MathCumulativeDistributionNoncentralChiSquare(const double &x[],const double nu,const double sigma,const bool tail,const bool log_mode,double &result[])
{
//--- check NaN
if(!MathIsValidNumber(nu) || !MathIsValidNumber(sigma))
return false;
//--- check arguments
if(nu!=MathRound(nu) || nu<=0.0)
return false;
int data_count=ArraySize(x);
if(data_count==0)
return false;
//--- common factors
double lambda=sigma*0.5;
double coef_lambda=MathExp(-lambda);
double half_nu=nu*0.5;
const int max_terms=100;
ArrayResize(result,data_count);
for(int i=0; i<data_count; i++)
{
double x_arg=x[i];
if(x_arg<=0.0)
result[i]=TailLog0(tail,log_mode);
else
{
double pwr_lambda=1.0;
double fact_mult=1.0;
double half_x=x_arg*0.5;
double cdf=0.0;
int j=0;
//--- direct summation
while(j<max_terms)
{
if(j>0)
{
pwr_lambda*=lambda;
fact_mult/=j;
}
double coef1=coef_lambda*pwr_lambda*fact_mult;
double coef2=MathMin(MathGammaIncomplete(half_x,half_nu+j),1.0);
double dp=coef1*coef2;
cdf=cdf+dp;
if((dp/(cdf+10E-10))<10E-16)
break;
j++;
}
//---
if(j<max_terms)
{
//--- take into account round-off errors for probability
cdf=MathMin(cdf,1.0);
result[i]=TailLogValue(cdf,tail,log_mode);
}
else
return false;
}
}
return true;
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square cumulative distribution function (CDF) |
//+------------------------------------------------------------------+
//| The function calculates the cumulative distribution function of |
//| the Noncentral Chi-Square distribution with parameters nu and |
//| sigma for values in x. |
//| |
//| Arguments: |
//| x : Array with random variables |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| result : Array with calculated values |
//| |
//| Return value: |
//| true if successful, otherwise false. |
//+------------------------------------------------------------------+
bool MathCumulativeDistributionNoncentralChiSquare(const double &x[],const double nu,const double sigma,double &result[])
{
return MathCumulativeDistributionNoncentralChiSquare(x,nu,sigma,true,false,result);
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution quantile function(inverse CDF)|
//+------------------------------------------------------------------+
//| The function returns the inverse cumulative distribution |
//| function of Noncentral Chi-Square distribution with parameters |
//| nu and sigma for the desired probability. |
//| |
//| Arguments: |
//| probability : The desired probability |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| error_code : Variable for error code |
//| |
//| Return value: |
//| The value of the inverse cumulative distribution function of |
//| Noncentral Chi-Square distribution with parameters nu and sigma. |
//+------------------------------------------------------------------+
double MathQuantileNoncentralChiSquare(const double probability,const double nu,const double sigma,const bool tail,const bool log_mode,int &error_code)
{
if(log_mode==true)
{
if(probability==QNEGINF)
return 0.0;
}
//--- check NaN
if(!MathIsValidNumber(probability) || !MathIsValidNumber(nu) || !MathIsValidNumber(sigma))
{
error_code=ERR_ARGUMENTS_NAN;
return QNaN;
}
//--- check arguments
if(nu!=MathRound(nu) || nu<=0.0)
{
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;
if(prob==0.0)
return 0.0;
if(prob==1.0)
return QPOSINF;
error_code=ERR_OK;
//--- common factors for pdf and cdf calculation
const int max_terms=1000;
double lambda=sigma*0.5;
double half_nu=nu*0.5;
double coef_lambda=MathExp(-lambda);
double half_nu_m1=half_nu-1.0;
double coef_gamma=1.0/MathGamma(half_nu);
double pwr_two2=MathExp(-half_nu*MathLog(2));
double pwr_half_num1=(half_nu-1.0);
//--- prepare values for initial x estimation
double x=0.5;
double h=1.0;
double h_min=10E-10;
//--- Newton iterations
const int max_iterations=50;
int iterations=0;
// int err_code=0;
while(iterations<max_iterations)
{
//--- check convergence
if((MathAbs(h)>h_min && MathAbs(h)>MathAbs(h_min*x))==false)
break;
//double pdf=MathProbabilityDensityNoncentralChiSquare(x,nu,sigma,false,err_code);
double half_x=x*0.5;
double pwr_lambda=1.0;
double pwr_two=pwr_two2;
double pwr_x=MathPow(x,pwr_half_num1);
double fact_mult=1.0;
double coef_lambda_x=coef_lambda*MathExp(-half_x);
double inv_factor=1.0;
//--- calculate density using direct summation
int j=0;
double pdf=0;
while(j<max_terms)
{
if(j>0)
{
pwr_lambda*=lambda;
pwr_x*=x;
pwr_two*=0.5;
fact_mult*=1.0/j;
inv_factor*=1.0/(j+half_nu-1);
}
double dp=coef_gamma*inv_factor*pwr_lambda*pwr_two*pwr_x*fact_mult*coef_lambda_x;
pdf=pdf+dp;
//--- check stop
if(dp/(pdf+10E-10)<10E-16)
break;
j++;
}
//--- check convergence
if(j>max_terms)
{
error_code=ERR_NON_CONVERGENCE;
return QNaN;
}
//--- calculate cdf
pwr_lambda=1.0;
fact_mult=1.0;
double cdf=0.0;
j=0;
//--- direct summation
while(j<max_terms)
{
if(j>0)
{
pwr_lambda*=lambda;
fact_mult/=j;
}
double coef1=coef_lambda*pwr_lambda*fact_mult;
double coef2=MathMin(MathGammaIncomplete(half_x,half_nu+j),1.0);
double dp=coef1*coef2;
cdf=cdf+dp;
if((dp/(cdf+10E-10))<10E-16)
break;
j++;
}
//---
if(j>max_terms)
{
error_code=ERR_NON_CONVERGENCE;
return QNaN;
}
//--- calculate ratio
h=(cdf-prob)/pdf;
double x_new=x-h;
if(x_new<0.0)
x_new=x*0.1;
else
if(x_new>1.0)
x_new=1.0-(1-x)*0.1;
x=x_new;
iterations++;
}
//--- check convergence
if(iterations<max_iterations)
return x;
else
{
error_code=ERR_NON_CONVERGENCE;
return QNaN;
}
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution quantile function(inverse CDF)|
//+------------------------------------------------------------------+
//| The function returns the inverse cumulative distribution |
//| function of the Noncentral Chi-Square distribution |
//| with parameters mu and sigma for the desired probability. |
//| |
//| Arguments: |
//| probability : The desired probability |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| error_code : Variable for error code |
//| |
//| Return value: |
//| The value of the inverse cumulative distribution function of |
//| Noncentral Chi-Square distribution with parameters mu and sigma. |
//+------------------------------------------------------------------+
double MathQuantileNoncentralChiSquare(const double probability,const double nu,const double sigma,int &error_code)
{
return MathQuantileNoncentralChiSquare(probability,nu,sigma,true,false,error_code);
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution quantile function(inverse CDF)|
//+------------------------------------------------------------------+
//| The function calculates the inverse cumulative distribution |
//| function of the Noncentral Chi-Square distribution with |
//| parameters nu and sigma for values from the probability[] array. |
//| |
//| Arguments: |
//| probability : Array with probabilities |
//| nu : Degrees of freedom |
//| sigma : Noncentrality 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 MathQuantileNoncentralChiSquare(const double &probability[],const double nu,const double sigma,const bool tail,const bool log_mode,double &result[])
{
//--- check NaN
if(!MathIsValidNumber(nu) || !MathIsValidNumber(sigma))
return false;
//--- check arguments
if(nu!=MathRound(nu) || nu<=0.0)
return false;
int data_count=ArraySize(probability);
if(data_count==0)
return false;
//--- common factors for pdf and cdf calculation
double lambda=sigma*0.5;
double half_nu=nu*0.5;
double pwr_two0=MathExp(-half_nu*MathLog(2));
double pwr_gamma0=1.0/MathGamma(half_nu);
double coef_lambda=MathExp(-lambda);
double half_nu_m1=half_nu-1.0;
const int max_terms=1000;
const int max_iterations=50;
double h_min=10E-10;
ArrayResize(result,data_count);
for(int i=0; i<data_count; i++)
{
//--- calculate real probability
double prob=TailLogProbability(probability[i],tail,log_mode);
if(prob==0.0)
result[i]=0.0;
else
if(prob==1.0)
result[i]=QPOSINF;
else
{
//--- check probability range
if(prob<0.0 || prob>1.0)
return false;
//--- prepare values for initial x estimation
int err_code=0;
double x=0.5;
double h=1.0;
//--- Newton iterations
int iterations=0;
while(iterations<max_iterations)
{
//--- check convergence
if((MathAbs(h)>h_min && MathAbs(h)>MathAbs(h_min*x))==false)
break;
//double pdf=MathProbabilityDensityNoncentralChiSquare(x,nu,sigma,false,err_code);
double half_x=x*0.5;
double pwr_lambda=1.0;
double pwr_two=pwr_two0;
double pwr_x=MathPow(x,half_nu_m1);
double fact_mult=1.0;
double coef_lambda_x=coef_lambda*MathExp(-half_x);
double inv_factor=1.0;
//--- calculate density using direct summation
int j=0;
double pdf=0;
while(j<max_terms)
{
if(j>0)
{
pwr_lambda*=lambda;
pwr_x*=x;
pwr_two*=0.5;
fact_mult*=1.0/j;
inv_factor*=1.0/(j+half_nu-1);
}
double dp=pwr_gamma0*inv_factor*pwr_lambda*pwr_two*pwr_x*fact_mult*coef_lambda_x;
pdf=pdf+dp;
//--- check stop
if(dp/(pdf+10E-10)<10E-16)
break;
j++;
}
//--- check convergence
if(j>max_terms)
return false;
//--- calculate cdf
pwr_lambda=1.0;
fact_mult=1.0;
pwr_lambda=1.0;
fact_mult=1.0;
double cdf=0.0;
j=0;
//--- direct summation
while(j<max_terms)
{
if(j>0)
{
pwr_lambda*=lambda;
fact_mult/=j;
}
double coef1=coef_lambda*pwr_lambda*fact_mult;
double coef2=MathMin(MathGammaIncomplete(half_x,half_nu+j),1.0);
double dp=coef1*coef2;
cdf=cdf+dp;
if((dp/(cdf+10E-10))<10E-16)
break;
j++;
}
//---
if(j>max_terms)
return false;
//--- calculate ratio
h=(cdf-prob)/pdf;
double x_new=x-h;
if(x_new<0.0)
x_new=x*0.1;
else
if(x_new>1.0)
x_new=1.0-(1-x)*0.1;
x=x_new;
iterations++;
}
//--- check convergence
if(iterations<max_iterations)
result[i]=x;
else
return false;
}
}
return true;
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution quantile function(inverse CDF)|
//+------------------------------------------------------------------+
//| The function calculates the inverse cumulative distribution |
//| function of the Noncentral Chi-Square distribution with |
//| parameters nu and sigma for values from the probability[] array. |
//| |
//| Arguments: |
//| probability : Array with probabilities |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| result : Array with calculated values |
//| |
//| Return value: |
//| true if successful, otherwise false. |
//+------------------------------------------------------------------+
bool MathQuantileNoncentralChiSquare(const double &probability[],const double nu,const double sigma,double &result[])
{
return MathQuantileNoncentralChiSquare(probability,nu,sigma,true,false,result);
}
//+------------------------------------------------------------------+
//| Random variate from the Noncentral Chi-Square distribution |
//+------------------------------------------------------------------+
//| Compute the random variable from the Noncentral Chi-Square |
//| distribution with parameters nu and sigma. |
//| |
//| Arguments: |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| error_code : Variable for error code |
//| |
//| Return value: |
//| The random value with Noncentral Chi-Square distribution. |
//+------------------------------------------------------------------+
//| Author: Robert Kern |
//+------------------------------------------------------------------+
double MathRandomNoncentralChiSquare(const double nu,const double sigma,int &error_code)
{
//--- return ChiSquare if sigma==0
if(sigma==0.0)
{
return MathRandomChiSquare(nu,error_code);
}
//--- check NaN
if(!MathIsValidNumber(nu) || !MathIsValidNumber(sigma))
{
error_code=ERR_ARGUMENTS_NAN;
return QNaN;
}
//--- check nu
if(nu!=MathRound(nu) || nu<=0)
{
error_code=ERR_ARGUMENTS_INVALID;
return QNaN;
}
//--- check sigma
if(sigma<0.0)
{
error_code=ERR_ARGUMENTS_INVALID;
return QNaN;
}
error_code=ERR_OK;
int err_code=0;
if(nu>1.0)
{
double rnd_chisquare=MathRandomGamma((nu-1)*0.5,2.0,err_code);
double rnd_normal=MathSqrt(sigma)+MathRandomNormal(0,1,err_code);
return rnd_chisquare+rnd_normal*rnd_normal;
}
else
{
int rnd_poisson=(int)MathRandomPoisson(sigma*0.5);
return MathRandomChiSquare(nu+2*rnd_poisson,err_code);
}
}
//+------------------------------------------------------------------+
//| Random variate from the Noncentral Chi-Square distribution |
//+------------------------------------------------------------------+
//| Generates random variables from the Noncentral Chi-Square |
//| distribution with parameters nu and sigma. |
//| |
//| Arguments: |
//| nu : Degrees of freedom |
//| sigma : Noncentrality parameter |
//| data_count : Number of values needed |
//| result : Output array with random values |
//| |
//| Return value: |
//| true if successful, otherwise false. |
//+------------------------------------------------------------------+
//| Author: Robert Kern |
//+------------------------------------------------------------------+
bool MathRandomNoncentralChiSquare(const double nu,const double sigma,const int data_count,double &result[])
{
//--- return ChiSquare if sigma==0
if(sigma==0.0)
return MathRandomChiSquare(nu,data_count,result);
//--- check NaN
if(!MathIsValidNumber(nu) || !MathIsValidNumber(sigma))
return false;
//--- check nu
if(nu!=MathRound(nu) || nu<=0)
return false;
//--- check sigma
if(sigma<0.0)
return false;
int err_code=0;
//--- prepare output array and calculate random values
ArrayResize(result,data_count);
for(int i=0; i<data_count; i++)
{
if(nu>1.0)
{
double rnd_chisquare=MathRandomGamma((nu-1)*0.5,2.0,err_code);
double rnd_normal=MathSqrt(sigma)+MathRandomNormal(0,1,err_code);
result[i]=rnd_chisquare+rnd_normal*rnd_normal;
}
else
{
int rnd_poisson=(int)MathRandomPoisson(sigma*0.5);
result[i]=MathRandomChiSquare(nu+2*rnd_poisson,err_code);
}
}
return true;
}
//+------------------------------------------------------------------+
//| Noncentral Chi-Square distribution moments |
//+------------------------------------------------------------------+
//| The function calculates 4 first moments of Noncental Chi-Square |
//| distribution with parameters nu and sigma. |
//| |
//| Arguments: |
//| nu : Degrees of freedom |
//| sigma : Noncentrality 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 MathMomentsNoncentralChiSquare(const double nu,const double sigma,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) || !MathIsValidNumber(sigma))
{
error_code=ERR_ARGUMENTS_NAN;
return false;
}
//--- check nu
if(nu!=MathRound(nu) || nu<=0.0)
{
error_code=ERR_ARGUMENTS_INVALID;
return false;
}
error_code=ERR_OK;
//--- calculate moments
mean =nu+sigma;
variance=2*nu+4*sigma;
skewness=2*M_SQRT2*(nu+3*sigma)*MathPow(nu+2*sigma,-1.5);
kurtosis=12*(nu+4*sigma)*MathPow(nu+2*sigma,-2);
//--- successful
return true;
}
//+------------------------------------------------------------------+
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