{
"cells": [
{
"cell_type": "markdown",
"id": "15adbd58",
"metadata": {},
"source": [
"# pdf001_Normal\n",
"Tutorial illustrating the new statistical distributions functions (pdf, cdf and quantile)\n",
"\n",
"based on Anna Kreshuk's normalDist.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": "39a538c0",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:28.553002Z",
"iopub.status.busy": "2026-05-19T20:26:28.552885Z",
"iopub.status.idle": "2026-05-19T20:26:29.561741Z",
"shell.execute_reply": "2026-05-19T20:26:29.560983Z"
}
},
"outputs": [],
"source": [
"from ROOT import TF1, TCanvas, TSystem, TAxis, TLegend\n",
"from ROOT import kRed, kGreen, kBlue"
]
},
{
"cell_type": "markdown",
"id": "5390438a",
"metadata": {},
"source": [
"Create the one dimensional functions for normal distribution."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "9ca54007",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:29.563299Z",
"iopub.status.busy": "2026-05-19T20:26:29.563165Z",
"iopub.status.idle": "2026-05-19T20:26:29.702442Z",
"shell.execute_reply": "2026-05-19T20:26:29.701723Z"
}
},
"outputs": [],
"source": [
"pdfunc = TF1(\"pdf\",\"ROOT::Math::normal_pdf(x, [0],[1])\", -5, 5)\n",
"cdfunc = TF1(\"cdf\",\"ROOT::Math::normal_cdf(x, [0],[1])\", -5, 5)\n",
"ccdfunc = TF1(\"cdf_c\",\"ROOT::Math::normal_cdf_c(x, [0])\", -5, 5)\n",
"qfunc = TF1(\"quantile\",\"ROOT::Math::normal_quantile(x, [0])\", 0, 1)\n",
"cqfunc = TF1(\"quantile_c\",\"ROOT::Math::normal_quantile_c(x, [0])\", 0, 1)"
]
},
{
"cell_type": "markdown",
"id": "9f35d3b3",
"metadata": {},
"source": [
"Set the parameters for the normal distribution with sigma to 1 and mean to\n",
"zero. And set the color to blue and title to none."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e3374d08",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:29.704484Z",
"iopub.status.busy": "2026-05-19T20:26:29.704356Z",
"iopub.status.idle": "2026-05-19T20:26:29.821070Z",
"shell.execute_reply": "2026-05-19T20:26:29.820240Z"
}
},
"outputs": [],
"source": [
"pdfunc.SetParameters(1.0, 0.0)\n",
"pdfunc.SetTitle(\"\")\n",
"pdfunc.SetLineColor(kBlue)"
]
},
{
"cell_type": "markdown",
"id": "5591eafe",
"metadata": {},
"source": [
"Set the configuration for the X and Y axis."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b7e6c079",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:29.822845Z",
"iopub.status.busy": "2026-05-19T20:26:29.822684Z",
"iopub.status.idle": "2026-05-19T20:26:29.939443Z",
"shell.execute_reply": "2026-05-19T20:26:29.938766Z"
}
},
"outputs": [],
"source": [
"Xaxis = pdfunc.GetXaxis()\n",
"Yaxis = pdfunc.GetYaxis()\n",
"Xaxis.SetLabelSize(0.06)\n",
"Xaxis.SetTitle(\"x\")\n",
"Xaxis.SetTitleSize(0.07)\n",
"Xaxis.SetTitleOffset(0.55)\n",
"Yaxis.SetLabelSize(0.06)"
]
},
{
"cell_type": "markdown",
"id": "cc0a92bd",
"metadata": {},
"source": [
"Set sigma to 1 and mean to zero, for the cumulative normal distribution, and\n",
"set the color to red and title to none."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "4b6adc32",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:29.941799Z",
"iopub.status.busy": "2026-05-19T20:26:29.941672Z",
"iopub.status.idle": "2026-05-19T20:26:30.045095Z",
"shell.execute_reply": "2026-05-19T20:26:30.044412Z"
}
},
"outputs": [],
"source": [
"cdfunc.SetParameters(1.0, 0.0)\n",
"cdfunc.SetTitle(\"\")\n",
"cdfunc.SetLineColor(kRed)"
]
},
{
"cell_type": "markdown",
"id": "d305fc10",
"metadata": {},
"source": [
"Set the configuration for the X and Y axis for the cumulative normal\n",
"distribution."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "d26d4532",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.047019Z",
"iopub.status.busy": "2026-05-19T20:26:30.046893Z",
"iopub.status.idle": "2026-05-19T20:26:30.150810Z",
"shell.execute_reply": "2026-05-19T20:26:30.150139Z"
}
},
"outputs": [],
"source": [
"cdXaxis = cdfunc.GetXaxis()\n",
"cdYaxis = cdfunc.GetYaxis()\n",
"cdXaxis.SetLabelSize(0.06)\n",
"cdXaxis.SetTitle(\"x\")\n",
"cdXaxis.SetTitleSize(0.07)\n",
"cdXaxis.SetTitleOffset(0.55)\n",
"cdYaxis.SetLabelSize(0.06)\n",
"cdYaxis.SetTitle(\"p\")\n",
"cdYaxis.SetTitleSize(0.07)\n",
"cdYaxis.SetTitleOffset(0.55)"
]
},
{
"cell_type": "markdown",
"id": "1b9004ae",
"metadata": {},
"source": [
"Set sigma to 1 and mean to zero, for the survival function of normal\n",
"distribution, and set the color to green and title to none"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f63722a1",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.152938Z",
"iopub.status.busy": "2026-05-19T20:26:30.152815Z",
"iopub.status.idle": "2026-05-19T20:26:30.256368Z",
"shell.execute_reply": "2026-05-19T20:26:30.255648Z"
}
},
"outputs": [],
"source": [
"ccdfunc.SetParameters(1.0, 0.0)\n",
"ccdfunc.SetTitle(\"\")\n",
"ccdfunc.SetLineColor(kGreen)"
]
},
{
"cell_type": "markdown",
"id": "205b8361",
"metadata": {},
"source": [
"Set sigma to 1 and mean to zero, for the quantile of normal distribution\n",
"To get more precision for p close to 0 or 1, set Npx to 1000"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "69ddaf6f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.258347Z",
"iopub.status.busy": "2026-05-19T20:26:30.258222Z",
"iopub.status.idle": "2026-05-19T20:26:30.368093Z",
"shell.execute_reply": "2026-05-19T20:26:30.367392Z"
}
},
"outputs": [],
"source": [
"qfunc.SetParameter(0, 1.0)\n",
"qfunc.SetTitle(\"\")\n",
"qfunc.SetLineColor(kRed)\n",
"qfunc.SetNpx(1000)"
]
},
{
"cell_type": "markdown",
"id": "6f74aeb4",
"metadata": {},
"source": [
"Set the configuration of X and Y axis"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "f645bf07",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.370075Z",
"iopub.status.busy": "2026-05-19T20:26:30.369952Z",
"iopub.status.idle": "2026-05-19T20:26:30.473974Z",
"shell.execute_reply": "2026-05-19T20:26:30.473164Z"
}
},
"outputs": [],
"source": [
"qfXaxis = qfunc.GetXaxis()\n",
"qfYaxis = qfunc.GetYaxis()\n",
"qfXaxis.SetLabelSize(0.06)\n",
"qfXaxis.SetTitle(\"p\")\n",
"qfYaxis.SetLabelSize(0.06)\n",
"qfXaxis.SetTitleSize(0.07)\n",
"qfXaxis.SetTitleOffset(0.55)\n",
"qfYaxis.SetTitle(\"x\")\n",
"qfYaxis.SetTitleSize(0.07)\n",
"qfYaxis.SetTitleOffset(0.55)"
]
},
{
"cell_type": "markdown",
"id": "a9d11b14",
"metadata": {},
"source": [
"Set sigma to 1 and mean to zero of survival function of quantile of normal\n",
"distribution, and set color to green and title to none."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "817e4bd7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.475951Z",
"iopub.status.busy": "2026-05-19T20:26:30.475825Z",
"iopub.status.idle": "2026-05-19T20:26:30.579325Z",
"shell.execute_reply": "2026-05-19T20:26:30.578645Z"
}
},
"outputs": [],
"source": [
"cqfunc.SetParameter(0, 1.0)\n",
"cqfunc.SetTitle(\"\")\n",
"cqfunc.SetLineColor(kGreen)\n",
"cqfunc.SetNpx(1000)"
]
},
{
"cell_type": "markdown",
"id": "dfc86395",
"metadata": {},
"source": [
"Create canvas and divide in three parts"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "d9509895",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.581114Z",
"iopub.status.busy": "2026-05-19T20:26:30.580985Z",
"iopub.status.idle": "2026-05-19T20:26:30.705313Z",
"shell.execute_reply": "2026-05-19T20:26:30.704596Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c1 = TCanvas(\"c1\", \"Normal Distributions\", 100, 10, 600, 800)\n",
"c1.Divide(1, 3)\n",
"c1.cd(1)"
]
},
{
"cell_type": "markdown",
"id": "ef73dcdc",
"metadata": {},
"source": [
"Draw the normal distribution"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "2c436997",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.707154Z",
"iopub.status.busy": "2026-05-19T20:26:30.707027Z",
"iopub.status.idle": "2026-05-19T20:26:30.823927Z",
"shell.execute_reply": "2026-05-19T20:26:30.823503Z"
}
},
"outputs": [],
"source": [
"pdfunc.Draw()\n",
"legend1 = TLegend(0.583893, 0.601973, 0.885221, 0.854151)\n",
"legend1.AddEntry(pdfunc, \"normal_pdf\", \"l\")\n",
"legend1.Draw()"
]
},
{
"cell_type": "markdown",
"id": "2363e168",
"metadata": {},
"source": [
"Draw the cumulative normal distribution"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "d4362874",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.836366Z",
"iopub.status.busy": "2026-05-19T20:26:30.836231Z",
"iopub.status.idle": "2026-05-19T20:26:30.939902Z",
"shell.execute_reply": "2026-05-19T20:26:30.939475Z"
}
},
"outputs": [],
"source": [
"c1.cd(2)\n",
"cdfunc.Draw()\n",
"ccdfunc.Draw(\"same\")\n",
"legend2 = TLegend(0.585605, 0.462794, 0.886933, 0.710837)\n",
"legend2.AddEntry(cdfunc, \"normal_cdf\", \"l\")\n",
"legend2.AddEntry(ccdfunc, \"normal_cdf_c\", \"l\")\n",
"legend2.Draw()"
]
},
{
"cell_type": "markdown",
"id": "e7c3b240",
"metadata": {},
"source": [
"Draw the normal quantile of normal distribution"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "fb4bcda0",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:30.952443Z",
"iopub.status.busy": "2026-05-19T20:26:30.952306Z",
"iopub.status.idle": "2026-05-19T20:26:31.056118Z",
"shell.execute_reply": "2026-05-19T20:26:31.055575Z"
}
},
"outputs": [],
"source": [
"c1.cd(3)\n",
"qfunc.Draw()\n",
"cqfunc.Draw(\"same\")\n",
"legend3 = TLegend(0.315094, 0.633668, 0.695179, 0.881711)\n",
"legend3.AddEntry(qfunc, \"normal_quantile\", \"l\")\n",
"legend3.AddEntry(cqfunc, \"normal_quantile_c\", \"l\")\n",
"legend3.Draw()"
]
},
{
"cell_type": "markdown",
"id": "a8302f43",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "6b2d8086",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:26:31.057911Z",
"iopub.status.busy": "2026-05-19T20:26:31.057788Z",
"iopub.status.idle": "2026-05-19T20:26:31.280697Z",
"shell.execute_reply": "2026-05-19T20:26:31.280175Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\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"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.12"
}
},
"nbformat": 4,
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}