void LLExp(){

  // Exponential model
  gStyle->SetOptStat(0);
  gStyle->SetOptFit(1111);
  gStyle->SetLabelSize(0.05,"XY");
  gStyle->SetTitleSize(0.05,"XYZ");
  gStyle->SetTitleOffset(1,"XYZ");

   // Model
	double fmin = 0;
	double fmax = 20;
	TF1 *fg = new TF1("fg", "([1]/[0])*TMath::Exp(-x/[0])", fmin, fmax);
	double tau = 2;
	fg->SetParameter(0, tau);
	fg->SetParameter(1, 1);
	fg->SetNpx(1000);

	// hist
	TH1F *hg = new TH1F("hg", "", 100, fmin, fmax);
	hg->SetMarkerStyle(20); hg->GetXaxis()->SetTitle("x"); hg->GetYaxis()->SetTitle("Events");

	// Generate sample
	int Nsample = 200;
	double tau_hat = 0;
	for (int j = 0; j < Nsample; j++){
		double t = fg->GetRandom();
		hg->Fill(t);
		tau_hat += t / Nsample;
	}

	// LL
	double fmin = 0;
	double fmax = 20;
	TF1 *fll = new TF1("fll", "-[0]*log(x) - [0]*[1]/x", 0.001, 6);
	fll->SetParameter(0, Nsample);
	fll->SetParameter(1, tau_hat);
	fll->SetNpx(1000);
	fll->GetXaxis()->SetTitle("#tau"); fll->GetYaxis()->SetTitle("Log L(#tau)");

	cout << "Mean = " << tau_hat << endl;

	new TCanvas(); hg->Draw("e1"); fg->SetParameter(1, Nsample*hg->GetBinWidth(1)); fg->Draw("same");
	new TCanvas(); fll->Draw();
}

void LLGaus(){

	// Gaus model
	gStyle->SetOptStat(0);
	gStyle->SetOptFit(1111);
	gStyle->SetLabelSize(0.05, "XY");
	gStyle->SetTitleSize(0.05, "XYZ");
	gStyle->SetTitleOffset(1, "XYZ");

	// Model
	double mux = 0;
	double sigmax = 1;
	TF1 *fg = new TF1("fg", "[0]*TMath::Gaus(x,[1],[2])", -5, 5);
	fg->SetParameters(1. / (sqrt(2 * TMath::Pi())*sigmax), mux, sigmax);
	fg->GetXaxis()->SetTitle("x"); fg->GetYaxis()->SetTitle("f_{x}(x)");
	fg->SetTitle("");
	fg->SetLineColor(2);
	fg->SetNpx(1000);

	// hist
	TH1F *hg = new TH1F("hg", "", 100, -5, 5);
	hg->SetMarkerStyle(20); hg->GetXaxis()->SetTitle("x"); hg->GetYaxis()->SetTitle("Events");

	// Generate sample
	int Nsample = 1000;
	double mu_hat = 0;
	double mu2_hat = 0;
	double sigma_hat = 0;
	for (int j = 0; j < Nsample; j++){
		double t = fg->GetRandom();
		hg->Fill(t);
		mu_hat += t / Nsample;
		mu2_hat += pow(t,2) / Nsample;
	}
	sigma_hat = sqrt(mu2_hat - pow(mu_hat, 2));

	cout << "Mean = " << mu_hat << ", sigma = " << sigma_hat << endl;

	// LL
	double fxmin = -0.5;
	double fxmax = 0.5;
	double fymin = 0.8;
	double fymax = 1.2;
	TF2 *fll = new TF2("fll", "-1*[0]*log(sqrt(2*TMath::Pi())*y) - [0]/(2*y*y)*([1]-x*x)",fxmin,fxmax,fymin,fymax);
	fll->SetParameter(0, Nsample);
	fll->SetParameter(1, mu2_hat);
	fll->SetNpx(1000);
	fll->GetXaxis()->SetTitle("#mu"); fll->GetYaxis()->SetTitle("#sigma"); fll->GetZaxis()->SetTitle("Log L");	

	new TCanvas(); hg->Draw("e1"); fg->SetParameter(0, Nsample*hg->GetBinWidth(1) / (sqrt(2 * TMath::Pi())*sigmax)); fg->Draw("same");
	new TCanvas(); fll->Draw("surf2");
	new TCanvas(); fll->Draw("cont1z");
}