/// \file

/// \ingroup tutorial_math

/// \notebook

/// Tutorial illustrating the new statistical distributions functions (pdf, cdf and quantile)

///

/// \macro_image

/// \macro_code

///

/// \author Anna Kreshuk

#include "Math/DistFunc.h"

#include "TF1.h"

#include "TCanvas.h"

#include "TSystem.h"

#include "TLegend.h"

#include "TAxis.h"

void normalDist() {

TF1 *pdfunc = new TF1("pdf","ROOT::Math::normal_pdf(x, [0],[1])",-5,5);

TF1 *cdfunc = new TF1("cdf","ROOT::Math::normal_cdf(x, [0],[1])",-5,5);

TF1 *ccdfunc = new TF1("cdf_c","ROOT::Math::normal_cdf_c(x, [0])",-5,5);

TF1 *qfunc = new TF1("quantile","ROOT::Math::normal_quantile(x, [0])",0,1);

TF1 *cqfunc = new TF1("quantile_c","ROOT::Math::normal_quantile_c(x, [0])",0,1);

pdfunc->SetParameters(1.0,0.0); // set sigma to 1 and mean to zero

pdfunc->SetTitle("");

pdfunc->SetLineColor(kBlue);

pdfunc->GetXaxis()->SetLabelSize(0.06);

pdfunc->GetXaxis()->SetTitle("x");

pdfunc->GetXaxis()->SetTitleSize(0.07);

pdfunc->GetXaxis()->SetTitleOffset(0.55);

pdfunc->GetYaxis()->SetLabelSize(0.06);

cdfunc->SetParameters(1.0,0.0); // set sigma to 1 and mean to zero

cdfunc->SetTitle("");

cdfunc->SetLineColor(kRed);

cdfunc->GetXaxis()->SetLabelSize(0.06);

cdfunc->GetXaxis()->SetTitle("x");

cdfunc->GetXaxis()->SetTitleSize(0.07);

cdfunc->GetXaxis()->SetTitleOffset(0.55);

cdfunc->GetYaxis()->SetLabelSize(0.06);

cdfunc->GetYaxis()->SetTitle("p");

cdfunc->GetYaxis()->SetTitleSize(0.07);

cdfunc->GetYaxis()->SetTitleOffset(0.55);

ccdfunc->SetParameters(1.0,0.0); // set sigma to 1 and mean to zero

ccdfunc->SetTitle("");

ccdfunc->SetLineColor(kGreen);

qfunc->SetParameter(0, 1.0); // set sigma to 1

qfunc->SetTitle("");

qfunc->SetLineColor(kRed);

qfunc->SetNpx(1000); // to get more precision for p close to 0 or 1

qfunc->GetXaxis()->SetLabelSize(0.06);

qfunc->GetXaxis()->SetTitle("p");

qfunc->GetYaxis()->SetLabelSize(0.06);

qfunc->GetXaxis()->SetTitleSize(0.07);

qfunc->GetXaxis()->SetTitleOffset(0.55);

qfunc->GetYaxis()->SetTitle("x");

qfunc->GetYaxis()->SetTitleSize(0.07);

qfunc->GetYaxis()->SetTitleOffset(0.55);

cqfunc->SetParameter(0, 1.0); // set sigma to 1

cqfunc->SetTitle("");

cqfunc->SetLineColor(kGreen);

cqfunc->SetNpx(1000);

TCanvas * c1 = new TCanvas("c1","Normal Distributions",100,10,600,800);

c1->Divide(1,3);

c1->cd(1);

pdfunc->Draw();

TLegend *legend1 = new TLegend(0.583893,0.601973,0.885221,0.854151);

legend1->AddEntry(pdfunc,"normal_pdf","l");

legend1->Draw();

c1->cd(2);

cdfunc->Draw();

ccdfunc->Draw("same");

TLegend *legend2 = new TLegend(0.585605,0.462794,0.886933,0.710837);

legend2->AddEntry(cdfunc,"normal_cdf","l");

legend2->AddEntry(ccdfunc,"normal_cdf_c","l");

legend2->Draw();

c1->cd(3);

qfunc->Draw();

cqfunc->Draw("same");

TLegend *legend3 = new TLegend(0.315094,0.633668,0.695179,0.881711);

legend3->AddEntry(qfunc,"normal_quantile","l");

legend3->AddEntry(cqfunc,"normal_quantile_c","l");

legend3->Draw();

}