[RF] Add RooStudent location-scale student's t-distribution

Fixes #21284

Original idea from Kirill Ivanov

Author: ferdymercury

README/ReleaseNotes/v640/index.md

@@ -192,6 +192,8 @@ As part of this migration, the following build options are deprecated. From ROOT
 
 ## RooFit
 
+- A new RooAbsPdf has been added: `RooStudentT`, which describes the location-scale student's t-distribution.
+
 ## RDataFrame
 
 - The message shown in ROOT 6.38 to inform users about change of default compression setting used by Snapshot (was 101 before 6.38, became 505 in 6.38) is now removed.

roofit/roofit/CMakeLists.txt

@@ -70,6 +70,7 @@ ROOT_STANDARD_LIBRARY_PACKAGE(RooFit
     RooPyBind.h
     RooSpline.h
     RooStepFunction.h
+    RooStudentT.h
     RooTFnBinding.h
     RooTFnPdfBinding.h
     RooTMathReg.h
@@ -134,6 +135,7 @@ ROOT_STANDARD_LIBRARY_PACKAGE(RooFit
     src/RooPolynomial.cxx
     src/RooSpline.cxx
     src/RooStepFunction.cxx
+    src/RooStudentT.cxx
     src/RooTFnBinding.cxx
     src/RooTFnPdfBinding.cxx
     src/RooTMathReg.cxx

roofit/roofit/inc/LinkDef1.h

@@ -24,6 +24,7 @@
 #pragma link C++ class RooPowerSum+ ;
 #pragma link C++ class RooGaussExpTails+ ;
 #pragma link C++ class RooGaussian+ ;
+#pragma link C++ class RooStudentT+ ;
 #pragma link C++ class RooLognormal+ ;
 #pragma link C++ class RooGamma+ ;
 #pragma link C++ class RooGaussModel+ ;

roofit/roofit/inc/RooStudentT.h

@@ -0,0 +1,47 @@
+#ifndef RooFit_RooFit_RooStudentT_h
+#define RooFit_RooFit_RooStudentT_h
+
+#include "RooAbsPdf.h"
+#include "RooRealProxy.h"
+
+class RooAbsReal;
+
+class RooStudentT : public RooAbsPdf {
+public:
+   RooStudentT() {};
+   RooStudentT(const char *name, const char *title, RooAbsReal::Ref x, RooAbsReal::Ref mean, RooAbsReal::Ref sigma,
+               RooAbsReal::Ref ndf);
+   RooStudentT(const RooStudentT &other, const char *name = nullptr);
+   TObject *clone(const char *newname = nullptr) const override { return new RooStudentT(*this, newname); }
+
+   Int_t getAnalyticalIntegral(RooArgSet &allVars, RooArgSet &analVars, const char *rangeName = nullptr) const override;
+   double analyticalIntegral(Int_t code, const char *rangeName = nullptr) const override;
+
+   /// Get the _x variable.
+   RooAbsReal const &x() const { return _x.arg(); }
+
+   /// Get the _mean parameter.
+   RooAbsReal const &mean() const { return _mean.arg(); }
+
+   /// Get the standard deviation parameter.
+   RooAbsReal const &sigma() const { return _sigma.arg(); }
+
+   /// Get the degrees of freedom parameter.
+   RooAbsReal const &ndf() const { return _ndf.arg(); }
+
+   Int_t getMaxVal(const RooArgSet &vars) const override;
+   double maxVal(Int_t code) const override;
+
+protected:
+   double evaluate() const override;
+
+private:
+   RooRealProxy _x;     ///< variable
+   RooRealProxy _mean;  ///< mean
+   RooRealProxy _sigma; ///< standard deviation
+   RooRealProxy _ndf;   ///< degrees of freedom
+
+   ClassDefOverride(RooStudentT, 1) // Location-scale Student's t-distribution PDF
+};
+
+#endif

roofit/roofit/src/RooStudentT.cxx

@@ -0,0 +1,71 @@
+/**
+ * \class RooStudentT
+ * \ingroup Roofit
+ *
+ * Location-scale Student's t-distribution
+ * \see https://en.wikipedia.org/wiki/Student's_t-distribution#Location-scale_t-distribution
+ */
+
+#include "RooStudentT.h"
+#include "RooHelpers.h"
+
+#include "TMath.h"
+
+RooStudentT::RooStudentT(const char *name, const char *title, RooAbsReal::Ref x, RooAbsReal::Ref mean,
+                         RooAbsReal::Ref sigma, RooAbsReal::Ref ndf)
+   : RooAbsPdf(name, title),
+     _x("x", "Observable", this, x),
+     _mean("mean", "Mean", this, mean),
+     _sigma("sigma", "Width", this, sigma),
+     _ndf("ndf", " Degrees of freedom", this, ndf)
+{
+   RooHelpers::checkRangeOfParameters(this, {&static_cast<RooAbsReal &>(sigma)}, 0);
+   RooHelpers::checkRangeOfParameters(this, {&static_cast<RooAbsReal &>(ndf)}, 1);
+}
+
+RooStudentT::RooStudentT(const RooStudentT &other, const char *name)
+   : RooAbsPdf(other, name),
+     _x("x", this, other._x),
+     _mean("mean", this, other._mean),
+     _sigma("sigma", this, other._sigma),
+     _ndf("ndf", this, other._ndf)
+{
+}
+
+double RooStudentT::evaluate() const
+{
+   const double t = (_x - _mean) / _sigma;
+   return TMath::Student(t, _ndf);
+}
+
+Int_t RooStudentT::getAnalyticalIntegral(RooArgSet &allVars, RooArgSet &analVars, const char * /*rangeName*/) const
+{
+   return matchArgs(allVars, analVars, _x) ? 1 : 0;
+}
+
+double RooStudentT::analyticalIntegral(Int_t code, const char *rangeName) const
+{
+   R__ASSERT(code == 1);
+
+   double tmin = (_x.min(rangeName) - _mean) / _sigma;
+   double tmax = (_x.max(rangeName) - _mean) / _sigma;
+   return (TMath::StudentI(tmax, _ndf) - TMath::StudentI(tmin, _ndf)) * _sigma;
+}
+
+/// Advertise that we know the maximum of self for given (mean,ndf,sigma).
+Int_t RooStudentT::getMaxVal(const RooArgSet &vars) const
+{
+   RooArgSet dummy;
+
+   if (matchArgs(vars, dummy, _x)) {
+      return 1;
+   }
+   return 0;
+}
+
+double RooStudentT::maxVal(Int_t code) const
+{
+   R__ASSERT(code == 1);
+
+   return TMath::Student(0, _ndf);
+}