Consolidate Python ignore rules into root gitignore
This commit is contained in:
Hiroaki86
@@ -0,0 +1,635 @@
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//+------------------------------------------------------------------+
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//| Lognormal.mqh |
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//| Copyright 2000-2026, MetaQuotes Ltd. |
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//| www.mql5.com |
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//+------------------------------------------------------------------+
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#include "Math.mqh"
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#include "Normal.mqh"
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//+------------------------------------------------------------------+
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//| Lognormal density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function |
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//| of the Lognormal distribution with parameters mu and sigma. |
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//| |
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//| f(x,mu,sigma)=[1/(x*sigma*sqrt(2pi)]*exp(-(ln(x)-mu)/(2*sigma^2))|
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| mu : Log mean |
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//| sigma : Log standard deviation |
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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 MathProbabilityDensityLognormal(const double x,const double mu,const double sigma,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(mu) || !MathIsValidNumber(sigma))
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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 sigma
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if(sigma<0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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error_code=ERR_OK;
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//--- check x
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if(x<=0.0)
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return TailLog0(true,log_mode);
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//--- check case sigma==0
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if(sigma==0)
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{
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if(MathLog(MathAbs(x))==mu)
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{
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error_code=ERR_RESULT_INFINITE;
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return QPOSINF;
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}
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else
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return TailLog0(true,log_mode);
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}
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//--- prepare argument
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double y=(MathLog(x)-mu)/sigma;
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//--- check argument
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if(!MathIsValidNumber(y))
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- check overflow
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y=MathAbs(y);
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if(y>=2*MathSqrt(DBL_MAX))
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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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//--- return lognormal density
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return TailLogValue(M_1_SQRT_2PI*MathExp(-0.5*y*y)/(x*sigma),true,log_mode);
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}
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//+------------------------------------------------------------------+
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//| Lognormal density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of |
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//| the Lognormal distribution with parameters mu and sigma |
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//| 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 : Log mean |
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//| sigma : Log standard deviation |
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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 MathProbabilityDensityLognormal(const double &x[],const double mu,const double sigma,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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return false;
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//--- check sigma
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if(sigma<0)
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return false;
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int data_count=ArraySize(x);
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if(data_count==0)
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return false;
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int error_code=0;
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ArrayResize(result,data_count);
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//--- check case sigma==0
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if(sigma==0)
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{
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for(int i=0; i<data_count; i++)
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{
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if(MathLog(MathAbs(x[i]))==mu)
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result[i]=QPOSINF;
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else
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result[i]=TailLog0(true,log_mode);
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return true;
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}
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}
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for(int i=0; i<data_count; i++)
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{
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double x_arg=x[i];
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if(!MathIsValidNumber(x_arg))
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return false;
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//--- check x
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if(x_arg<=0.0)
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result[i]=TailLog0(true,log_mode);
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else
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{
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//--- prepare argument
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double y=(MathLog(x_arg)-mu)/sigma;
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//--- check argument
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if(!MathIsValidNumber(y))
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return false;
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//--- check overflow
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y=MathAbs(y);
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if(y>=2*MathSqrt(DBL_MAX))
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return false;
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//--- return lognormal density
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result[i]=TailLogValue(M_1_SQRT_2PI*MathExp(-0.5*y*y)/(x_arg*sigma),true,log_mode);
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}
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Lognormal density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function calculates the probability density function of |
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//| the Lognormal distribution with parameters mu and sigma |
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//| for values in x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| mu : Log mean |
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//| sigma : Log standard deviation |
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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 MathProbabilityDensityLognormal(const double &x[],const double mu,const double sigma,double &result[])
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{
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return MathProbabilityDensityLognormal(x,mu,sigma,false,result);
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}
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//+------------------------------------------------------------------+
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//| Lognormal density function (PDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability density function |
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//| of the Lognormal distribution with parameters mu and sigma. |
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//| |
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//| f(x,mu,sigma)=[1/(x*sigma*sqrt(2pi)]*exp(-(ln(x)-mu)/(2*sigma^2))|
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//| |
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//| Arguments: |
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//| x : Random variable |
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//| mu : Log mean |
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//| sigma : Log standard deviation |
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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 MathProbabilityDensityLognormal(const double x,const double mu,const double sigma,int &error_code)
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{
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return MathProbabilityDensityLognormal(x,mu,sigma,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Lognormal cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability that an observation |
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//| from the Lognormal distribution with parameters mu and sigma |
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//| is less than or equal to x. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| mu : Log mean |
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//| sigma : Log standard deviation |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode, if true it calculates Log values |
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//| error_code : Variable for error code |
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//| |
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//| Return value: |
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//| The value of the Lognormal cumulative distribution function |
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//| with parameters mu and sigma, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionLognormal(const double x,const double mu,const double sigma,const bool tail,const bool log_mode,int &error_code)
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{
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//--- check NaN
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if(!MathIsValidNumber(x) || !MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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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 sigma
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if(sigma<0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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error_code=ERR_OK;
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//--- check x
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if(x<=0.0)
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return TailLog0(tail,log_mode);
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//--- return lognormal cdf using Normal cdf
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return MathCumulativeDistributionNormal(MathLog(x),mu,sigma,tail,log_mode,error_code);
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}
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//+------------------------------------------------------------------+
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//| Lognormal cumulative distribution function (CDF) |
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//+------------------------------------------------------------------+
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//| The function returns the probability that an observation |
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//| from the Lognormal distribution with parameters mu and sigma |
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//| is less than or equal to x. |
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//| |
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//| Arguments: |
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//| x : The desired quantile |
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//| mu : Log mean |
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//| sigma : Log standard deviation |
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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 Lognormal cumulative distribution function |
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//| with parameters mu and sigma, evaluated at x. |
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//+------------------------------------------------------------------+
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double MathCumulativeDistributionLognormal(const double x,const double mu,const double sigma,int &error_code)
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{
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return MathCumulativeDistributionLognormal(x,mu,sigma,true,false,error_code);
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}
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//+------------------------------------------------------------------+
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//| Lognormal 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 Lognormal distribution with parameters mu and sigma |
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//| for values in x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| mu : Log mean |
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//| sigma : Log standard deviation |
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//| tail : Flag to calculate lower tail |
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//| log_mode : Logarithm mode, if true it calculates Log values |
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//| result : Array with calculated values |
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//| |
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//| Return value: |
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//| true if successful, otherwise false. |
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//+------------------------------------------------------------------+
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bool MathCumulativeDistributionLognormal(const double &x[],const double mu,const double sigma,const bool tail,const bool log_mode,double &result[])
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{
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//--- check NaN
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if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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return false;
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//--- check sigma
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if(sigma<0)
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return false;
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int data_count=ArraySize(x);
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if(data_count==0)
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return false;
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int error_code=0;
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ArrayResize(result,data_count);
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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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//--- check x
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if(x_arg<=0.0)
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result[i]=TailLog0(tail,log_mode);
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else
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//--- return lognormal cdf using Normal cdf
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result[i]=MathCumulativeDistributionNormal(MathLog(x_arg),mu,sigma,tail,log_mode,error_code);
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}
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return true;
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}
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//+------------------------------------------------------------------+
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//| Lognormal 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 Lognormal distribution with parameters mu and sigma |
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//| for values in x[] array. |
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//| |
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//| Arguments: |
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//| x : Array with random variables |
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//| mu : Log mean |
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//| sigma : Log standard deviation |
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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 MathCumulativeDistributionLognormal(const double &x[],const double mu,const double sigma,double &result[])
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{
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return MathCumulativeDistributionLognormal(x,mu,sigma,true,false,result);
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}
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//+------------------------------------------------------------------+
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//| Lognormal 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 Lognormal distribution with parameters mu |
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//| and sigma 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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//| mu : Log mean |
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//| sigma : Log standard deviation |
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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 quantile value of the Lognormal distribution. |
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//+------------------------------------------------------------------+
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double MathQuantileLognormal(const double probability,const double mu,const double sigma,const bool tail,const bool log_mode,int &error_code)
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{
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if(log_mode==true && probability==QNEGINF)
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{
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error_code=ERR_OK;
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return 0.0;
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}
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//--- check NaN
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if(!MathIsValidNumber(probability) || !MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
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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 sigma
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if(sigma<0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- calculate real probability
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double prob=TailLogProbability(probability,tail,log_mode);
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//--- check probability range
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if(prob<0.0 || prob>1.0)
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{
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error_code=ERR_ARGUMENTS_INVALID;
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return QNaN;
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}
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//--- special cases exp(a+b-+infinity)
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if(prob==0.0 || prob==1.0)
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{
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if(sigma==0.0)
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{
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error_code=ERR_OK;
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return MathExp(mu);
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}
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else
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if(prob==0.0)
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{
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if(sigma>0)
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{
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error_code=ERR_OK;
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return 0.0;
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}
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else
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if(sigma<0)
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{
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error_code=ERR_RESULT_INFINITE;
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return QPOSINF;
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}
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}
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else
|
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{
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if(sigma<0)
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{
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error_code=ERR_OK;
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return 0.0;
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}
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else
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if(sigma>0)
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{
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error_code=ERR_RESULT_INFINITE;
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return QPOSINF;
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}
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}
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}
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//--- return lognormal quantile using Normal distribution
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return MathExp(MathQuantileNormal(prob,mu,sigma,error_code));
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}
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//+------------------------------------------------------------------+
|
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//| Lognormal distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function returns the inverse cumulative distribution |
|
||||
//| function of Lognormal distribution with parameters mu and sigma |
|
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//| for the desired probability. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| probability : The desired probability |
|
||||
//| mu : Log mean |
|
||||
//| sigma : Log standard deviation |
|
||||
//| error_code : Variable for error code |
|
||||
//| |
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||||
//| Return value: |
|
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//| The quantile value of the Lognormal distribution. |
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//+------------------------------------------------------------------+
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double MathQuantileLognormal(const double probability,const double mu,const double sigma,int &error_code)
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{
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return MathQuantileLognormal(probability,mu,sigma,true,false,error_code);
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}
|
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//+------------------------------------------------------------------+
|
||||
//| Lognormal distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates the inverse cumulative distribution |
|
||||
//| function of the Lognormal distribution with parameters mu and |
|
||||
//| sigma for values from the probability[] array. |
|
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//| |
|
||||
//| Arguments: |
|
||||
//| probability : Array with probabilities |
|
||||
//| mu : Log mean |
|
||||
//| sigma : Log standard deviation |
|
||||
//| tail : Flag to calculate lower tail |
|
||||
//| log_mode : Logarithm mode,if true it calculates for 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 MathQuantileLognormal(const double &probability[],const double mu,const double sigma,const bool tail,const bool log_mode,double &result[])
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{
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//--- check NaN
|
||||
if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
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return false;
|
||||
//--- check sigma
|
||||
if(sigma<0)
|
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return false;
|
||||
|
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int data_count=ArraySize(probability);
|
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if(data_count==0)
|
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return false;
|
||||
|
||||
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;
|
||||
|
||||
//--- special cases exp(a+b-+infinity)
|
||||
if(prob==0.0 || prob==1.0)
|
||||
{
|
||||
if(sigma==0.0)
|
||||
result[i]=MathExp(mu);
|
||||
else
|
||||
if(prob==0.0)
|
||||
{
|
||||
if(sigma>0)
|
||||
result[i]=0.0;
|
||||
else
|
||||
if(sigma<0)
|
||||
result[i]=QPOSINF;
|
||||
}
|
||||
else
|
||||
{
|
||||
if(sigma<0)
|
||||
result[i]=0.0;
|
||||
else
|
||||
if(sigma>0)
|
||||
result[i]=QPOSINF;
|
||||
}
|
||||
}
|
||||
else
|
||||
//--- calculate lognormal quantile using Normal distribution
|
||||
result[i]=MathExp(MathQuantileNormal(prob,mu,sigma,error_code));
|
||||
}
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Lognormal distribution quantile function (inverse CDF) |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates the inverse cumulative distribution |
|
||||
//| function of the Lognormal distribution with parameters mu and |
|
||||
//| sigma for values from the probability[] array. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| probability : Array with probabilities |
|
||||
//| mu : Log mean |
|
||||
//| sigma : Log standard deviation |
|
||||
//| result : Array with calculated values |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if successful, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathQuantileLognormal(const double &probability[],const double mu,const double sigma,double &result[])
|
||||
{
|
||||
return MathQuantileLognormal(probability,mu,sigma,true,false,result);
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Lognormal distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Computes the random variable from the Lognormal distribution |
|
||||
//| with parameters mu and sigma. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| mu : Log mean |
|
||||
//| sigma : Log standard deviation |
|
||||
//| error_code : Variable for error code |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| The random value with Lognormal distribution. |
|
||||
//+------------------------------------------------------------------+
|
||||
double MathRandomLognormal(const double mu,const double sigma,int &error_code)
|
||||
{
|
||||
//--- check NaN
|
||||
if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_NAN;
|
||||
return QNaN;
|
||||
}
|
||||
//--- check sigma
|
||||
if(sigma<0)
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_INVALID;
|
||||
return QNaN;
|
||||
}
|
||||
error_code=ERR_OK;
|
||||
//--- generate random number
|
||||
double rnd=MathRandomNonZero();
|
||||
//---
|
||||
rnd=MathQuantileNormal(rnd,mu,sigma,true,false,error_code);
|
||||
return MathExp(rnd);
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Random variate from the Lognormal distribution |
|
||||
//+------------------------------------------------------------------+
|
||||
//| Generates random variables from the Lognormal distribution |
|
||||
//| with parameters mu and sigma. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| mu : Log mean |
|
||||
//| sigma : Log standard deviation |
|
||||
//| data_count : Number of values needed |
|
||||
//| result : Output array with random values |
|
||||
//| |
|
||||
//| Return value: |
|
||||
//| true if successful, otherwise false. |
|
||||
//+------------------------------------------------------------------+
|
||||
bool MathRandomLognormal(const double mu,const double sigma,const int data_count,double &result[])
|
||||
{
|
||||
//--- check NaN
|
||||
if(!MathIsValidNumber(mu) || !MathIsValidNumber(sigma))
|
||||
return false;
|
||||
//--- check sigma
|
||||
if(sigma<0)
|
||||
return false;
|
||||
//--- prepare output array and calculate random values
|
||||
ArrayResize(result,data_count);
|
||||
int err_code=0;
|
||||
for(int i=0; i<data_count; i++)
|
||||
result[i]=MathRandomNonZero();
|
||||
//--- return normal random array using quantile
|
||||
MathQuantileNormal(result,mu,sigma,result);
|
||||
return MathExp(result);
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
//| Lognormal distribution moments |
|
||||
//+------------------------------------------------------------------+
|
||||
//| The function calculates 4 first moments of the Lognormal |
|
||||
//| distribution with parameters mu and sigma. |
|
||||
//| |
|
||||
//| Arguments: |
|
||||
//| mu : Log mean |
|
||||
//| sigma : Log standard deviation |
|
||||
//| 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 MathMomentsLognormal(const double mu,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(mu) || !MathIsValidNumber(sigma))
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_NAN;
|
||||
return false;
|
||||
}
|
||||
//--- check sigma
|
||||
if(sigma<0)
|
||||
{
|
||||
error_code=ERR_ARGUMENTS_INVALID;
|
||||
return false;
|
||||
}
|
||||
|
||||
error_code=ERR_OK;
|
||||
//--- sigma squared
|
||||
double sigma_sqr=sigma*sigma;
|
||||
double exp_sigma_sqr=MathExp(sigma_sqr);
|
||||
//--- calculate moments
|
||||
mean =MathExp(mu+sigma_sqr*0.5);
|
||||
variance=(exp_sigma_sqr-1.0)*MathExp(2*mu+sigma_sqr);
|
||||
skewness=MathSqrt(exp_sigma_sqr-1.0)*(exp_sigma_sqr+2.0);
|
||||
kurtosis=3*MathPowInt(exp_sigma_sqr,2)+2*MathPowInt(exp_sigma_sqr,3)+MathPowInt(exp_sigma_sqr,4)-3-3;
|
||||
//--- successful
|
||||
return true;
|
||||
}
|
||||
//+------------------------------------------------------------------+
|
||||
Reference in New Issue
Block a user