{
"cells": [
{
"cell_type": "markdown",
"id": "385e5a32",
"metadata": {},
"source": [
"# pdf012_tStudent\n",
"Example macro describing the student t distribution\n",
"\n",
"```cpp\n",
"root[0]: .x tStudent.C\n",
"```\n",
"\n",
"It draws the pdf, the cdf and then 10 quantiles of the t Student distribution\n",
"\n",
"based on Magdalena Slawinska's tStudent.C\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Juan Fernando Jaramillo Botero \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": "code",
"execution_count": 1,
"id": "3c316762",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:27:02.758974Z"
}
},
"outputs": [],
"source": [
"from ROOT import TH1D, TF1, TCanvas, kRed, kBlue\n",
"import ROOT\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"id": "4a4a6b02",
"metadata": {},
"source": [
"This is the way to force load of MathMore in Cling"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "4dd64e40",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:02.761742Z",
"iopub.status.busy": "2026-05-19T20:27:02.761526Z",
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"shell.execute_reply": "2026-05-19T20:27:02.897173Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : libMathMore has been loaded.\n"
]
}
],
"source": [
"ROOT.Math.MathMoreLibrary.Load()"
]
},
{
"cell_type": "markdown",
"id": "62107aee",
"metadata": {},
"source": [
"Create the pdf and the cumulative distributions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ba788437",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:02.899626Z",
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"shell.execute_reply": "2026-05-19T20:27:03.021909Z"
}
},
"outputs": [],
"source": [
"n = 100\n",
"a = -5.\n",
"b = 5.\n",
"pdf = TF1(\"pdf\", \"ROOT::Math::tdistribution_pdf(x,3.0)\", a, b)\n",
"cum = TF1(\"cum\", \"ROOT::Math::tdistribution_cdf(x,3.0)\", a, b)"
]
},
{
"cell_type": "markdown",
"id": "73da9222",
"metadata": {},
"source": [
"Create the histogram and fill it with the quantiles"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "7bfa432e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:03.024666Z",
"iopub.status.busy": "2026-05-19T20:27:03.024516Z",
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"shell.execute_reply": "2026-05-19T20:27:03.144468Z"
}
},
"outputs": [],
"source": [
"quant = TH1D(\"quant\", \"\", 9, 0, 0.9)\n",
"\n",
"quant.Fill(\n",
" np.array([(i - 0.5) / 10.0 for i in range(1, 10)]),\n",
" np.array([ROOT.Math.tdistribution_quantile(0.1 * i, 3.0) for i in range(1, 10)]),\n",
")"
]
},
{
"cell_type": "markdown",
"id": "7accd606",
"metadata": {},
"source": [
"For each quantile fill with the pdf"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "8434e308",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:03.147225Z",
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"shell.execute_reply": "2026-05-19T20:27:03.276610Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning in : nbins is <=0 - set to nbins = 1\n"
]
}
],
"source": [
"xx = []\n",
"xx.append(-1.5)\n",
"for i in range(1, 9):\n",
" xx.append(quant.GetBinContent(i))\n",
"xx.append(1.5)\n",
"\n",
"pdfq = []\n",
"for i in range(9):\n",
" nbin = int(n * (xx[i+1] - xx[i]) / 3.0 + 1.0)\n",
" name = \"pdf%d\" % i\n",
" pdfq.append(TH1D(name, \"\", nbin, xx[i], xx[i+1]))\n",
" for j in range(1, nbin):\n",
" x = j * (xx[i+1] - xx[i]) / nbin + xx[i]\n",
" pdfq[i].SetBinContent(j, ROOT.Math.tdistribution_pdf(x, 3))"
]
},
{
"cell_type": "markdown",
"id": "c55f09d5",
"metadata": {},
"source": [
"Create the Canvas and divide in four draws, for every draw set the line width\n",
"the title, and the line color."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "a827a6bd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:03.279432Z",
"iopub.status.busy": "2026-05-19T20:27:03.279304Z",
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"shell.execute_reply": "2026-05-19T20:27:03.430360Z"
}
},
"outputs": [],
"source": [
"Canvas = TCanvas(\"DistCanvas\", \"Student Distribution graphs\", 10, 10, 800, 700)\n",
"pdf.SetTitle(\"Student t distribution function\")\n",
"cum.SetTitle(\"Cumulative for Student t\")\n",
"quant.SetTitle(\"10-quantiles for Student t\")\n",
"Canvas.Divide(2, 2)\n",
"Canvas.cd(1)\n",
"pdf.SetLineWidth(2)\n",
"pdf.DrawCopy()\n",
"Canvas.cd(2)\n",
"cum.SetLineWidth(2)\n",
"cum.SetLineColor(kRed)\n",
"cum.Draw()\n",
"Canvas.cd(3)\n",
"quant.Draw()\n",
"quant.SetLineWidth(2)\n",
"quant.SetLineColor(kBlue)\n",
"quant.SetStats(0)\n",
"Canvas.cd(4)\n",
"pdfq[0].SetTitle(\"Student t & its quantiles\")\n",
"pdf.SetTitle(\"\")\n",
"pdf.Draw()\n",
"pdfq[0].SetTitle(\"Student t & its quantiles\")"
]
},
{
"cell_type": "markdown",
"id": "bb87ed3b",
"metadata": {},
"source": [
"Set the colors in every quantile."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "9235c32c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:03.446872Z",
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"shell.execute_reply": "2026-05-19T20:27:03.555105Z"
}
},
"outputs": [],
"source": [
"i = 1\n",
"for pd in pdfq[1:]:\n",
" pd.SetStats(0)\n",
" i += 1\n",
" pd.SetFillColor(i)\n",
" pd.Draw(\"same\")\n",
"Canvas.Modified()"
]
},
{
"cell_type": "markdown",
"id": "7126f86e",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "1a9653c9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:03.557205Z",
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"outputs": [
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"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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