## \file

## \ingroup tutorial_math

## \notebook

## Tutorial illustrating the new statistical distributions functions (pdf, cdf and quantile)

##

## based on Anna Kreshuk's normalDist.C

##

## \macro_image

## \macro_code

##

## \author Juan Fernando Jaramillo Botero

from ROOT import TF1, TCanvas, TSystem, TAxis, TLegend

from ROOT import kRed, kGreen, kBlue

# Create the one dimentional functions for normal distribution.

pdfunc = TF1("pdf","ROOT::Math::normal_pdf(x, [0],[1])", -5, 5)

cdfunc = TF1("cdf","ROOT::Math::normal_cdf(x, [0],[1])", -5, 5)

ccdfunc = TF1("cdf_c","ROOT::Math::normal_cdf_c(x, [0])", -5, 5)

qfunc = TF1("quantile","ROOT::Math::normal_quantile(x, [0])", 0, 1)

cqfunc = TF1("quantile_c","ROOT::Math::normal_quantile_c(x, [0])", 0, 1)

# Set the parameters for the normal distribution with sigma to 1 and mean to

# zero. And set the color to blue and title to none.

pdfunc.SetParameters(1.0, 0.0)

pdfunc.SetTitle("")

pdfunc.SetLineColor(kBlue)

# Set the configuration for the X and Y axis.

Xaxis = pdfunc.GetXaxis()

Yaxis = pdfunc.GetYaxis()

Xaxis.SetLabelSize(0.06)

Xaxis.SetTitle("x")

Xaxis.SetTitleSize(0.07)

Xaxis.SetTitleOffset(0.55)

Yaxis.SetLabelSize(0.06)

# Set sigma to 1 and mean to zero, for the cumulative normal distribution, and

# set the color to red and title to none.

cdfunc.SetParameters(1.0, 0.0)

cdfunc.SetTitle("")

cdfunc.SetLineColor(kRed)

# Set the configuration for the X and Y axis for the cumulative normal

# distribution.

cdXaxis = cdfunc.GetXaxis()

cdYaxis = cdfunc.GetYaxis()

cdXaxis.SetLabelSize(0.06)

cdXaxis.SetTitle("x")

cdXaxis.SetTitleSize(0.07)

cdXaxis.SetTitleOffset(0.55)

cdYaxis.SetLabelSize(0.06)

cdYaxis.SetTitle("p")

cdYaxis.SetTitleSize(0.07)

cdYaxis.SetTitleOffset(0.55)

# Set sigma to 1 and mean to zero, for the survival function of normal

# distribution, and set the color to green and title to none

ccdfunc.SetParameters(1.0, 0.0)

ccdfunc.SetTitle("")

ccdfunc.SetLineColor(kGreen)

# Set sigma to 1 and mean to zero, for the quantile of normal distribution

# To get more precision for p close to 0 or 1, set Npx to 1000

qfunc.SetParameter(0, 1.0)

qfunc.SetTitle("")

qfunc.SetLineColor(kRed)

qfunc.SetNpx(1000)

# Set the configuration of X and Y axis

qfXaxis = qfunc.GetXaxis()

qfYaxis = qfunc.GetYaxis()

qfXaxis.SetLabelSize(0.06)

qfXaxis.SetTitle("p")

qfYaxis.SetLabelSize(0.06)

qfXaxis.SetTitleSize(0.07)

qfXaxis.SetTitleOffset(0.55)

qfYaxis.SetTitle("x")

qfYaxis.SetTitleSize(0.07)

qfYaxis.SetTitleOffset(0.55)

# Set sigma to 1 and mean to zero of survival function of quantile of normal

# distribution, and set color to green and title to none.

cqfunc.SetParameter(0, 1.0)

cqfunc.SetTitle("")

cqfunc.SetLineColor(kGreen)

cqfunc.SetNpx(1000)

# Create canvas and divide in three parts

c1 = TCanvas("c1", "Normal Distributions", 100, 10, 600, 800)

c1.Divide(1, 3)

c1.cd(1)

# Draw the normal distribution

pdfunc.Draw()

legend1 = TLegend(0.583893, 0.601973, 0.885221, 0.854151)

legend1.AddEntry(pdfunc, "normal_pdf", "l")

legend1.Draw()

# Draw the cumulative normal distribution

c1.cd(2)

cdfunc.Draw()

ccdfunc.Draw("same")

legend2 = TLegend(0.585605, 0.462794, 0.886933, 0.710837)

legend2.AddEntry(cdfunc, "normal_cdf", "l")

legend2.AddEntry(ccdfunc, "normal_cdf_c", "l")

legend2.Draw()

# Draw the normal quantile of normal distribution

c1.cd(3)

qfunc.Draw()

cqfunc.Draw("same")

legend3 = TLegend(0.315094, 0.633668, 0.695179, 0.881711)

legend3.AddEntry(qfunc, "normal_quantile", "l")

legend3.AddEntry(cqfunc, "normal_quantile_c", "l")

legend3.Draw()