289 lines
16 KiB
MQL5
289 lines
16 KiB
MQL5
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//+------------------------------------------------------------------+
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//| TestStatPrecision.mq5 |
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//| Copyright 2000-2025, MetaQuotes Ltd. |
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//| https://www.mql5.com |
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//+------------------------------------------------------------------+
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#property copyright "Copyright 2000-2025, MetaQuotes Ltd."
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#property link "https://www.mql5.com"
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#property version "1.00"
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#include <Math\Stat\Normal.mqh>
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#include <Math\Stat\Weibull.mqh>
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#include <Math\Stat\Uniform.mqh>
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#include <Math\Stat\Logistic.mqh>
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#include <Math\Stat\Cauchy.mqh>
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#include <Math\Stat\Exponential.mqh>
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#include <Math\Stat\Lognormal.mqh>
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#include <Math\Stat\Poisson.mqh>
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#include <Math\Stat\Gamma.mqh>
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#include <Math\Stat\Chisquare.mqh>
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#include <Math\Stat\NoncentralChisquare.mqh>
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#include <Math\Stat\Binomial.mqh>
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#include <Math\Stat\Beta.mqh>
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#include <Math\Stat\F.mqh>
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#include <Math\Stat\Geometric.mqh>
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#include <Math\Stat\T.mqh>
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#include <Math\Stat\Hypergeometric.mqh>
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#include <Math\Stat\NegativeBinomial.mqh>
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#include <Math\Stat\NoncentralBeta.mqh>
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#include <Math\Stat\NoncentralF.mqh>
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#include <Math\Stat\NoncentralT.mqh>
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//--- PDF and CDF values calculated with Wolfram Alpha (30 digits)
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//--- http://www.wolframalpha.com/input/?i=N%5BPDF%5BBetaDistribution%5B2,4%5D,0.5%5D,30%5D
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const double Wolfram_Beta_PDF = 1.25000000000000000000000000000; // N[PDF[BetaDistribution[2,4],0.5],30]
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const double Wolfram_Beta_CDF = 0.812500000000000000000000000000; // N[CDF[BetaDistribution[2,4],0.5],30]
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const double Wolfram_Binomial_PDF = 0.178863050569879740960000000000; // N[PDF[BinomialDistribution[20,0.3],5],30]
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const double Wolfram_Binomial_CDF = 0.416370829447481383720000000000; // N[CDF[BinomialDistribution[20,0.3],5],30]
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const double Wolfram_Cauchy_PDF = 0.0783532027529330883785273911988; // N[PDF[CauchyDistribution[2,1],0.25],30]
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const double Wolfram_Cauchy_CDF = 0.165249340538567909638346176210; // N[CDF[CauchyDistribution[2,1],0.25],30]
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const double Wolfram_ChiSquare_PDF = 0.389400391535702434122585133489; // N[PDF[ChiSquareDistribution[2],0.5],30]
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const double Wolfram_ChiSquare_CDF = 0.221199216928595131754829733022; // N[CDF[ChiSquareDistribution[2],0.5],30]
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const double Wolfram_Exponential_PDF = 0.441248451292297701432446071615; // N[PDF[ExponentialDistribution[1/2],0.25],30]
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const double Wolfram_Exponential_CDF = 0.117503097415404597135107856771; // N[CDF[ExponentialDistribution[1/2],0.25],30]
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const double Wolfram_F_PDF = 0.702331961591220850480109739369; // N[PDF[FRatioDistribution[2,4],0.25],30]
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const double Wolfram_F_CDF = 0.209876543209876543209876543210; // N[CDF[FRatioDistribution[2,4],0.25],30]
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const double Wolfram_Gamma_PDF = 0.606530659712633423603799534991; // N[PDF[GammaDistribution[1,1],0.5],30]
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const double Wolfram_Gamma_CDF = 0.393469340287366576396200465009; // N[CDF[GammaDistribution[1,1],0.5],30]
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const double Wolfram_Geometric_PDF = 0.0504210000000000000000000000000; // N[PDF[GeometricDistribution[0.3],5],30]
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const double Wolfram_Geometric_CDF = 0.882351000000000000000000000000; // N[CDF[GeometricDistribution[0.3],5],30]
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const double Wolfram_Hypergeometric_PDF = 0.0366753989045010716837342224339; // N[PDF[HypergeometricDistribution[9,8,20],6],30]
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const double Wolfram_Hypergeometric_CDF = 0.996784948797332698261490831150; // N[CDF[HypergeometricDistribution[9,8,20],6],30]
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const double Wolfram_Logistic_PDF = 0.235003712201594489069302695021; // N[PDF[LogisticDistribution[1,1],0.5],30]
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const double Wolfram_Logistic_CDF = 0.377540668798145435361099434254; // N[CDF[LogisticDistribution[1,1],0.5],30]
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const double Wolfram_Lognormal_PDF = 2.47498055546993572014793467512E-7; // N[PDF[LognormalDistribution[10,2],0.5],30]
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const double Wolfram_Lognormal_CDF = 4.48174235017131858935036726113E-8; // N[CDF[LognormalDistribution[10,2],0.5],30]
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const double Wolfram_NegativeBinomial_PDF = 0.0468750000000000000000000000000; // N[PDF[NegativeBinomialDistribution[2,0.5],5],30]
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const double Wolfram_NegativeBinomial_CDF = 0.937500000000000000000000000000; // N[CDF[NegativeBinomialDistribution[2,0.5],5],30]
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const double Wolfram_NoncentralBeta_PDF = 1.83531575828435897166952478333; // N[PDF[NoncentralBetaDistribution[2,4,1],0.25],30]
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const double Wolfram_NoncentralBeta_CDF = 0.279804451879309969773066407543; // N[CDF[NoncentralBetaDistribution[2,4,1],0.25],30]
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const double Wolfram_NoncentralChiSquare_PDF = 0.266641691212769080163425079921; // N[PDF[NoncentralChiSquareDistribution[2,1],0.5],30]
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const double Wolfram_NoncentralChiSquare_CDF = 0.142365913869366361026153686445; // N[CDF[NoncentralChiSquareDistribution[2,1],0.5],30]
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const double Wolfram_NoncentralF_PDF = 0.354683475208693741397782642610; // N[PDF[NoncentralFRatioDistribution[2,4,2],0.25],30]
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const double Wolfram_NoncentralF_CDF = 0.0907943467375269920219944143035; // N[CDF[NoncentralFRatioDistribution[2,4,2],0.25],30]
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const double Wolfram_Normal_PDF = 0.0000133655982673381195940786008171; // N[PDF[NormalDistribution[21,5],0.15],30]
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const double Wolfram_Normal_CDF = 0.0000152299819479778795518408747262; // N[CDF[NormalDistribution[21,5],0.15],30]
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const double Wolfram_Poisson_PDF = 2.81323432020839550168137707324E-13; // N[PDF[PoissonDistribution[1],15],30]
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const double Wolfram_Poisson_CDF = 0.99999999999998132236536831934; // N[CDF[PoissonDistribution[1],15],30]
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const double Wolfram_Uniform_PDF = 0.00400000000000000000000000000000; // N[PDF[UniformDistribution[0,250],0.125],30]
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const double Wolfram_Uniform_CDF = 0.000500000000000000000000000000000; // N[CDF[UniformDistribution[0,250],0.125],30]
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const double Wolfram_Weibull_PDF = 0.0195121858238667121530217146408; // N[PDF[WeibullDistribution[5,1],0.25],30]
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const double Wolfram_Weibull_CDF = 0.000976085818024337765288210389671; // N[CDF[WeibullDistribution[5,1],0.25],30]
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const double Wolfram_T_PDF = 0.319904796224811454367412653512; // N[PDF[TDistribution[4],0.51234567890123456],30]
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const double Wolfram_T_CDF = 0.6822990443550955053632292600646; // N[CDF[TDistribution[4],0.51234567890123456],30]
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const double Wolfram_NoncentralT_PDF = 4.06507868645014429884902547978E-14; // N[PDF[Noncentral T Distribution[10,8],0.25],30]
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const double Wolfram_NoncentralT_CDF = 4.81698E-15; // N[CDF[Noncentral T Distribution[10,8],0.25],30]
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//+------------------------------------------------------------------+
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//| GetCorrectDigits |
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//+------------------------------------------------------------------+
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int GetCorrectDigits(const double delta)
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{
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double d=MathAbs(delta);
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//--- check if delta to small
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if(d<10E-30)
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return(30);
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//--- check if delta is large
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if(d>=1.0)
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return(0);
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int correct_digits=0;
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while(MathAbs(d)<1.0)
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{
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d=d*10;
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correct_digits++;
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}
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//---
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return(correct_digits-1);
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}
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//+------------------------------------------------------------------+
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//| TestPrecision |
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//+------------------------------------------------------------------+
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void TestPrecision(const string comment,const double pdf,const double cdf,const double pdf_calculated,const double cdf_calculated)
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{
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double delta_pdf=pdf-pdf_calculated;
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double delta_cdf=cdf-cdf_calculated;
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//--- print results
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Print("Testing precision for distribution:",comment);
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//---- print results
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PrintFormat("Distribution: %s, Wolfram PDF=%6.30f, PDF_calculated=%6.30f, deltaPDF=%6.30f",comment,pdf,pdf_calculated,delta_pdf);
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PrintFormat("Distribution: %s, Wolfram CDF=%6.30f, CDF_calculated=%6.30f, deltaCDF=%6.30f",comment,cdf,cdf_calculated,delta_cdf);
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//--- print correct digits
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PrintFormat("Distribution: %s PDF correct digits=%d",comment,GetCorrectDigits(delta_pdf));
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PrintFormat("Distribution: %s CDF correct digits=%d",comment,GetCorrectDigits(delta_cdf));
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Print("");
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return;
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}
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//+------------------------------------------------------------------+
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//| Script program start function |
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//+------------------------------------------------------------------+
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void OnStart()
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{
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int error_code=0;
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//--- Beta distribution parameters
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double a=2.0;
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double b=4.0;
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double x=0.5;
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double d_beta = MathProbabilityDensityBeta(x, a, b,error_code);
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double p_beta = MathCumulativeDistributionBeta(x, a, b,error_code);
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TestPrecision("Beta",Wolfram_Beta_PDF,Wolfram_Beta_CDF,d_beta,p_beta);
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//--- Binomial distribution parameters
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x=5;
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double n=20;
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double prob=0.3;
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double d_binomial = MathProbabilityDensityBinomial(x,n,prob,error_code);
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double p_binomial = MathCumulativeDistributionBinomial(x,n,prob,error_code);
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TestPrecision("Binomial",Wolfram_Binomial_PDF,Wolfram_Binomial_CDF,d_binomial,p_binomial);
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//--- Cauchy distribution parameters
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x=0.25;
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a=2.0; //mean
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b=1.0; //scale
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double d_cauchy = MathProbabilityDensityCauchy(x,a,b,error_code);
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double p_cauchy = MathCumulativeDistributionCauchy(x,a,b,error_code);
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TestPrecision("Cauchy",Wolfram_Cauchy_PDF,Wolfram_Cauchy_CDF,d_cauchy,p_cauchy);
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//--- ChiSquare distribution parameters
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double nu=2;
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x=0.5;
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double d_chisquare = MathProbabilityDensityChiSquare(x,nu,error_code);
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double p_chisquare = MathCumulativeDistributionChiSquare(x,nu,error_code);
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TestPrecision("ChiSquare",Wolfram_ChiSquare_PDF,Wolfram_ChiSquare_CDF,d_chisquare,p_chisquare);
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//--- Exponential distribution parameters
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x=0.25;
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double mu=2.0; // scale
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double d_exp = MathProbabilityDensityExponential(x,mu,error_code);
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double p_exp = MathCumulativeDistributionExponential(x,mu,error_code);
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TestPrecision("Exponential",Wolfram_Exponential_PDF,Wolfram_Exponential_CDF,d_exp,p_exp);
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//--- F distribution parameters
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x=0.25;
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int nu1=2;
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int nu2=4;
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double d_F = MathProbabilityDensityF(x,nu1,nu2,error_code);
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double p_F = MathCumulativeDistributionF(x,nu1,nu2,error_code);
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TestPrecision("F",Wolfram_F_PDF,Wolfram_F_CDF,d_F,p_F);
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//--- Gamma distribution parameters
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x=0.5;
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a=1.0; // shape
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b=1.0; // scale
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double d_gamma = MathProbabilityDensityGamma(x,a,b,error_code);
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double p_gamma = MathCumulativeDistributionGamma(x,a,b,error_code);
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TestPrecision("Gamma",Wolfram_Gamma_PDF,Wolfram_Gamma_CDF,d_gamma,p_gamma);
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//--- Geometric distribution parameters
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x=5;
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prob=0.3;
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double d_geometric = MathProbabilityDensityGeometric(x,prob,error_code);
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double p_geometric = MathCumulativeDistributionGeometric(x,prob,error_code);
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TestPrecision("Geometric",Wolfram_Geometric_PDF,Wolfram_Geometric_CDF,d_geometric,p_geometric);
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//--- Hypergeometric distribution parameters
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x=6;
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double m=20;
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double k=8;
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n=9;
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double d_hypergeometric = MathProbabilityDensityHypergeometric(x,m,k,n,error_code);
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double p_hypergeometric = MathCumulativeDistributionHypergeometric(x,m,k,n,error_code);
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TestPrecision("Hypergeometric",Wolfram_Hypergeometric_PDF,Wolfram_Hypergeometric_CDF,d_hypergeometric,p_hypergeometric);
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//--- Logistic distribution parameters
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x=0.5;
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mu=1.0; // mean
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double sigma=1.0; // scale
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double d_logistic = MathProbabilityDensityLogistic(x,mu,sigma,error_code);
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double p_logistic = MathCumulativeDistributionLogistic(x,mu,sigma,error_code);
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TestPrecision("Logistic",Wolfram_Logistic_PDF,Wolfram_Logistic_CDF,d_logistic,p_logistic);
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//--- Lognormal distribution parameters
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x=0.5;
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mu=10.0;
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sigma=2.0;
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double d_lognormal = MathProbabilityDensityLognormal(x,mu,sigma,error_code);
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double p_lognormal = MathCumulativeDistributionLognormal(x,mu,sigma,error_code);
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TestPrecision("Lognormal",Wolfram_Lognormal_PDF,Wolfram_Lognormal_CDF,d_lognormal,p_lognormal);
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//--- Negative Binomial distribution parameters
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x=5.0;
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double r=2.0;
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prob=0.5;
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double d_negbinomial = MathProbabilityDensityNegativeBinomial(x,r,prob,error_code);
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double p_negbinomial = MathCumulativeDistributionNegativeBinomial(x,r,prob,error_code);
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TestPrecision("NegativeBinomial",Wolfram_NegativeBinomial_PDF,Wolfram_NegativeBinomial_CDF,d_negbinomial,p_negbinomial);
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//--- Noncentral Beta distribution parameters
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x=0.25;
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a=2.0;
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b=4.0;
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double lambda=1;
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double d_noncentralbeta = MathProbabilityDensityNoncentralBeta(x,a,b,lambda,error_code);
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double p_noncentralbeta = MathCumulativeDistributionNoncentralBeta(x,a,b,lambda,error_code);
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TestPrecision("NoncentralBeta",Wolfram_NoncentralBeta_PDF,Wolfram_NoncentralBeta_CDF,d_noncentralbeta,p_noncentralbeta);
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//--- Noncentral ChiSquare distribution parameters
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x=0.5;
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nu=2.0;
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sigma=1.0;
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double d_nchisquare = MathProbabilityDensityNoncentralChiSquare(x,nu,sigma,error_code);
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double p_nchisquare = MathCumulativeDistributionNoncentralChiSquare(x,nu,sigma,error_code);
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TestPrecision("NoncentralChiSquare",Wolfram_NoncentralChiSquare_PDF,Wolfram_NoncentralChiSquare_CDF,d_nchisquare,p_nchisquare);
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//--- Noncentral F distribution parameters
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x=0.25;
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nu1=2.0;
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nu2=4.0;
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sigma=2.0;
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double d_noncentralF = MathProbabilityDensityNoncentralF(x,nu1,nu2,sigma,error_code);
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double p_noncentralF = MathCumulativeDistributionNoncentralF(x,nu1,nu2,sigma,error_code);
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TestPrecision("NoncentralF",Wolfram_NoncentralF_PDF,Wolfram_NoncentralF_CDF,d_noncentralF,p_noncentralF);
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//--- Normal distribution parameters
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x=0.15;
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mu=21.0;
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sigma=5.0;
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double d_normal = MathProbabilityDensityNormal(x, mu, sigma,error_code);
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double p_normal = MathCumulativeDistributionNormal(x, mu, sigma,error_code);
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TestPrecision("Normal",Wolfram_Normal_PDF,Wolfram_Normal_CDF,d_normal,p_normal);
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//--- Poisson distribution parameters
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x=15;
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lambda=1.0;
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double d_poisson = MathProbabilityDensityPoisson(x,lambda,error_code);
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double p_poisson = MathCumulativeDistributionPoisson(x,lambda,error_code);
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TestPrecision("Poisson",Wolfram_Poisson_PDF,Wolfram_Poisson_CDF,d_poisson,p_poisson);
|
||
|
|
|
||
|
|
//--- Uniform distribution parameters
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||
|
|
x=0.125;
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||
|
|
a=0.0; // lower
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||
|
|
b=250.0; // upper
|
||
|
|
double d_uniform = MathProbabilityDensityUniform(x,a,b,error_code);
|
||
|
|
double p_uniform = MathCumulativeDistributionUniform(x,a,b,error_code);
|
||
|
|
TestPrecision("Uniform",Wolfram_Uniform_PDF,Wolfram_Uniform_CDF,d_uniform,p_uniform);
|
||
|
|
|
||
|
|
//--- Weibull distribution parameters
|
||
|
|
x=0.25;
|
||
|
|
a=5.0; // shape
|
||
|
|
b=1.0; // scale
|
||
|
|
double d_weibull = MathProbabilityDensityWeibull(x,a,b,error_code);
|
||
|
|
double p_weibull = MathCumulativeDistributionWeibull(x,a,b,error_code);
|
||
|
|
TestPrecision("Weibull",Wolfram_Weibull_PDF,Wolfram_Weibull_CDF,d_weibull,p_weibull);
|
||
|
|
|
||
|
|
//--- T distribution parameters
|
||
|
|
x=0.51234567890123456;
|
||
|
|
nu=4.0;
|
||
|
|
double d_T = MathProbabilityDensityT(x,nu,error_code);
|
||
|
|
double p_T = MathCumulativeDistributionT(x,nu,error_code);
|
||
|
|
TestPrecision("T",Wolfram_T_PDF,Wolfram_T_CDF,d_T,p_T);
|
||
|
|
|
||
|
|
//--- Noncentral T distribution parameters
|
||
|
|
x=0.25;
|
||
|
|
nu=10.0;
|
||
|
|
double delta=8.0;
|
||
|
|
double d_NT = MathProbabilityDensityNoncentralT(x,nu,delta,error_code);
|
||
|
|
double p_NT = MathCumulativeDistributionNoncentralT(x,nu,delta,error_code);
|
||
|
|
TestPrecision("NoncentralT",Wolfram_NoncentralT_PDF,Wolfram_NoncentralT_CDF,d_NT,p_NT);
|
||
|
|
}
|
||
|
|
//+------------------------------------------------------------------+
|