{
"cells": [
{
"cell_type": "markdown",
"id": "675ea593",
"metadata": {},
"source": [
"# pdf011_Student\n",
"Tutorial illustrating the use of the Student and F distributions\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Anna Kreshuk \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:26 PM."
]
},
{
"cell_type": "markdown",
"id": "7cb6fe7d",
"metadata": {},
"source": [
"drawing the set of student density functions\n",
"normal(0, 1) density drawn for comparison"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "67f4653b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:57.159715Z",
"iopub.status.busy": "2026-05-19T20:26:57.159584Z",
"iopub.status.idle": "2026-05-19T20:26:57.618565Z",
"shell.execute_reply": "2026-05-19T20:26:57.617775Z"
}
},
"outputs": [],
"source": [
"TCanvas *DistCanvas = new TCanvas(\"DistCanvas\", \"Distribution graphs\", 10, 10, 800, 650);\n",
"DistCanvas->SetFillColor(17);\n",
"DistCanvas->Divide(2, 2);\n",
"DistCanvas->cd(1);\n",
"gPad->SetGrid();\n",
"gPad->SetFrameFillColor(19);\n",
"TLegend *leg = new TLegend(0.6, 0.7, 0.89, 0.89);\n",
"\n",
"\n",
"TF1* fgaus = new TF1(\"gaus\", \"TMath::Gaus(x, [0], [1], [2])\", -5, 5);\n",
"fgaus->SetTitle(\"Student density\");\n",
"fgaus->SetLineStyle(kDashed);\n",
"fgaus->SetLineWidth(1);\n",
"fgaus->SetParameters(0, 1, kTRUE);\n",
"leg->AddEntry(fgaus->DrawCopy(), \"Normal(0,1)\", \"l\");\n",
"\n",
"TF1* student = new TF1(\"student\", \"TMath::Student(x,[0])\", -5, 5);"
]
},
{
"cell_type": "markdown",
"id": "46cf8883",
"metadata": {},
"source": [
"student->SetTitle(\"Student density\");"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "bcc4b235",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:57.620301Z",
"iopub.status.busy": "2026-05-19T20:26:57.620180Z",
"iopub.status.idle": "2026-05-19T20:26:57.827244Z",
"shell.execute_reply": "2026-05-19T20:26:57.826542Z"
}
},
"outputs": [],
"source": [
"student->SetLineWidth(1);\n",
"student->SetParameter(0, 10);\n",
"student->SetLineColor(4);\n",
"leg->AddEntry(student->DrawCopy(\"lsame\"), \"10 degrees of freedom\", \"l\");\n",
"\n",
"student->SetParameter(0, 3);\n",
"student->SetLineColor(2);\n",
"leg->AddEntry(student->DrawCopy(\"lsame\"), \"3 degrees of freedom\", \"l\");\n",
"\n",
"student->SetParameter(0, 1);\n",
"student->SetLineColor(1);\n",
"leg->AddEntry(student->DrawCopy(\"lsame\"), \"1 degree of freedom\", \"l\");\n",
"\n",
"leg->Draw();"
]
},
{
"cell_type": "markdown",
"id": "3dba7ac6",
"metadata": {},
"source": [
"drawing the set of student cumulative probability functions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "d9c673a1",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:57.829200Z",
"iopub.status.busy": "2026-05-19T20:26:57.829082Z",
"iopub.status.idle": "2026-05-19T20:26:58.036124Z",
"shell.execute_reply": "2026-05-19T20:26:58.035340Z"
}
},
"outputs": [],
"source": [
"DistCanvas->cd(2);\n",
"gPad->SetFrameFillColor(19);\n",
"gPad->SetGrid();\n",
"TF1 *studentI = new TF1(\"studentI\", \"TMath::StudentI(x, [0])\", -5, 5);\n",
"studentI->SetTitle(\"Student cumulative dist.\");\n",
"studentI->SetLineWidth(1);\n",
"TLegend *leg2 = new TLegend(0.6, 0.4, 0.89, 0.6);\n",
"\n",
"studentI->SetParameter(0, 10);\n",
"studentI->SetLineColor(4);\n",
"leg2->AddEntry(studentI->DrawCopy(), \"10 degrees of freedom\", \"l\");\n",
"\n",
"studentI->SetParameter(0, 3);\n",
"studentI->SetLineColor(2);\n",
"leg2->AddEntry(studentI->DrawCopy(\"lsame\"), \"3 degrees of freedom\", \"l\");\n",
"\n",
"studentI->SetParameter(0, 1);\n",
"studentI->SetLineColor(1);\n",
"leg2->AddEntry(studentI->DrawCopy(\"lsame\"), \"1 degree of freedom\", \"l\");\n",
"leg2->Draw();"
]
},
{
"cell_type": "markdown",
"id": "b4349d98",
"metadata": {},
"source": [
"drawing the set of F-dist. densities"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "63a6f8b7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:58.037899Z",
"iopub.status.busy": "2026-05-19T20:26:58.037780Z",
"iopub.status.idle": "2026-05-19T20:26:58.244624Z",
"shell.execute_reply": "2026-05-19T20:26:58.243981Z"
}
},
"outputs": [],
"source": [
"TF1* fDist = new TF1(\"fDist\", \"TMath::FDist(x, [0], [1])\", 0, 2);\n",
"fDist->SetTitle(\"F-Dist. density\");\n",
"fDist->SetLineWidth(1);\n",
"TLegend* legF1 = new TLegend(0.7, 0.7, 0.89, 0.89);\n",
"\n",
"DistCanvas->cd(3);\n",
"gPad->SetFrameFillColor(19);\n",
"gPad->SetGrid();\n",
"\n",
"fDist->SetParameters(1, 1);\n",
"fDist->SetLineColor(1);\n",
"legF1->AddEntry(fDist->DrawCopy(), \"N=1 M=1\", \"l\");\n",
"\n",
"fDist->SetParameter(1, 10);\n",
"fDist->SetLineColor(2);\n",
"legF1->AddEntry(fDist->DrawCopy(\"lsame\"), \"N=1 M=10\", \"l\");\n",
"\n",
"fDist->SetParameters(10, 1);\n",
"fDist->SetLineColor(8);\n",
"legF1->AddEntry(fDist->DrawCopy(\"lsame\"), \"N=10 M=1\", \"l\");\n",
"\n",
"fDist->SetParameters(10, 10);\n",
"fDist->SetLineColor(4);\n",
"legF1->AddEntry(fDist->DrawCopy(\"lsame\"), \"N=10 M=10\", \"l\");\n",
"\n",
"legF1->Draw();"
]
},
{
"cell_type": "markdown",
"id": "80402dcb",
"metadata": {},
"source": [
"drawing the set of F cumulative dist.functions"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "daeada02",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:58.246743Z",
"iopub.status.busy": "2026-05-19T20:26:58.246619Z",
"iopub.status.idle": "2026-05-19T20:26:58.453200Z",
"shell.execute_reply": "2026-05-19T20:26:58.452778Z"
}
},
"outputs": [],
"source": [
"TF1* fDistI = new TF1(\"fDist\", \"TMath::FDistI(x, [0], [1])\", 0, 2);\n",
"fDistI->SetTitle(\"Cumulative dist. function for F\");\n",
"fDistI->SetLineWidth(1);\n",
"TLegend* legF2 = new TLegend(0.7, 0.3, 0.89, 0.5);\n",
"\n",
"DistCanvas->cd(4);\n",
"gPad->SetFrameFillColor(19);\n",
"gPad->SetGrid();\n",
"fDistI->SetParameters(1, 1);\n",
"fDistI->SetLineColor(1);\n",
"legF2->AddEntry(fDistI->DrawCopy(), \"N=1 M=1\", \"l\");\n",
"\n",
"fDistI->SetParameters(1, 10);\n",
"fDistI->SetLineColor(2);\n",
"legF2->AddEntry(fDistI->DrawCopy(\"lsame\"), \"N=1 M=10\", \"l\");\n",
"\n",
"fDistI->SetParameters(10, 1);\n",
"fDistI->SetLineColor(8);\n",
"legF2->AddEntry(fDistI->DrawCopy(\"lsame\"), \"N=10 M=1\", \"l\");\n",
"\n",
"fDistI->SetParameters(10, 10);\n",
"fDistI->SetLineColor(4);\n",
"legF2->AddEntry(fDistI->DrawCopy(\"lsame\"), \"N=10 M=10\", \"l\");\n",
"\n",
"legF2->Draw();\n",
"DistCanvas->cd();"
]
},
{
"cell_type": "markdown",
"id": "30c4c33f",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "e48d5942",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:58.455154Z",
"iopub.status.busy": "2026-05-19T20:26:58.455044Z",
"iopub.status.idle": "2026-05-19T20:26:58.767413Z",
"shell.execute_reply": "2026-05-19T20:26:58.766955Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gROOT->GetListOfCanvases()->Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "ROOT C++",
"language": "c++",
"name": "root"
},
"language_info": {
"codemirror_mode": "text/x-c++src",
"file_extension": ".C",
"mimetype": " text/x-c++src",
"name": "c++"
}
},
"nbformat": 4,
"nbformat_minor": 5
}