Dear experts.

I was asked to do a test hypothesis but I don’t really know what I’m doing, I’ll explain myself.

I have a distribution “genpdf” from which I sample a dataset. I’m then asked to do a statistical test on that data with respect to the genpdf itself and to a uniform distribution. Here is the code I use for creating the uniform pdf and the genpdf from which I sample data:

```
RooRealVar t("t","t",0,2*M_PI) ;
RooRealVar p("p","p", 0, M_PI) ;
//Defining Parameters according to RooFit.
//Initial value is the 3rd argument, 4th and 5th arg
//are the range of existance of the parameter.
RooRealVar alpha("alpha", "alpha", 0.65, 0.6, 0.7);
RooRealVar beta("beta", "beta", 0.06, 0, 0.1);
RooRealVar gamma("gamma", "gamma", -0.18, -0.2, -0.16);
RooRealVar scale("scale", "scale", 1., 0, 10);
RooRealVar scale_uni("scale_uni", "scale_uni", 1.);
RooRealVar for_comp("for_comp", "for_comp", 0.1, 0, 1);
RooUniform uni_t("uniformt", "uniformt", t);
RooUniform uni_p("uniformp", "uniformp", p);
//UNIFORM PDF
RooAddPdf unif("unif", "uni_t+uni_p", RooArgList(uni_t, uni_p), RooArgList(scale_uni));
//ClassFactory generates a pdf instance and normalize it.
RooAbsPdf* genpdf = RooClassFactory::makePdfInstance("GenPdf","scale*(3./(4.*M_PI))*(0.5*(1.-alpha) + (0.5)*(3.*alpha-1)*cos(t)*cos(t) - beta*sin(t)*sin(t)*cos(2.*p)- sqrt(2.)*gamma*sin(2.*t)*cos(p))",RooArgSet(t,p,alpha, beta, gamma, scale)) ;
RooDataSet* data = genpdf->generate(RooArgSet(t,p), 50000);
```

The genpdf reduces to a uniform distribution when alpha=1/3, beta=0, gamma=0.

For the statistical test I built the following pdf as summing the genpdf and the uniform one with a proportionality parameter “for_comp”:

```
RooAddPdf zero_meno("zero_meno", "gen_pdf+uniform", RooArgList(*genpdf,unif), RooArgList(for_comp) );
```

After checking that everything works ok (I fitted zero_mean to the data using unbind ML fit, as expected to returned only the gen_pdf setting the uniform at 0) I create the workspace needed for the test:

```
RooWorkspace*w = new RooWorkspace("w");
w->import(t);
w->import(p);
w->import(zero_meno);
w->import(*data);
w->defineSet("obs",RooArgSet(t,p));
w->defineSet("poi",RooArgSet(for_comp));
w->defineSet("nuisParams","alpha, beta, gamma, scale");
ModelConfig zero_model("zero_model", w);
zero_model.SetPdf(*w->pdf("zero_meno"));
zero_model.SetObservables(*w->set("obs"));
zero_model.SetParametersOfInterest(*w->set("poi"));
w->var("for_comp")->setVal(0.0); // important only uniform
zero_model.SetSnapshot(*w->set("poi"));
// create the alternate (signal+background) ModelConfig with s=50
ModelConfig uno_model("uno_model", w);
uno_model.SetPdf(*w->pdf("zero_meno"));
uno_model.SetObservables(*w->set("obs"));
uno_model.SetParametersOfInterest(*w->set("poi"));
w->var("for_comp")->setVal(0.5); // Setting non zero value to genpdf
uno_model.SetSnapshot(*w->set("poi"));
```

Then I create a frequentist calculator and define the ProfileLikelihood as test statistics and run the HypoTest:

```
FrequentistCalculator * fc = new FrequentistCalculator(*data, zero_model, uno_model);
fc->SetToys(1000,1000); // 1000 for null (B) and 1000 for alt (S+B)
// create the test statistics
ProfileLikelihoodTestStat profll(*uno_model.GetPdf());
// use one-sided profile likelihood
profll.SetOneSidedDiscovery(true);
// configure ToyMCSampler and set the test statistics
ToyMCSampler *toymcs = (ToyMCSampler*)fc->GetTestStatSampler();
toymcs->SetTestStatistic(&profll);
//Not sure about this
if (!uno_model.GetPdf()->canBeExtended())
toymcs->SetNEventsPerToy(1);
// run the test
HypoTestResult * res = fc->GetHypoTest();
res->Print();
```

This action has no end and it keeps iterating (waited 20m and no results). Furthermore this message keeps appearing:

```
[#0] ERROR:Eval -- RooAbsReal::logEvalError(GenPdf) evaluation error,
origin : RooGenPdfPdf::GenPdf[ t=t p=p alpha=alpha beta=beta gamma=gamma scale=scale ]
message : p.d.f value is less than zero (-0.000048), forcing value to zero
```

The fact is, most of this code is taken from various examples of S+B over B models. I don’t know if this class also applies to my problem, if so am I doing it right? Is this the right way to use RooStats for the problem?

Thank you, have a nice day.