normalDist.py File Reference

Detailed Description

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

based on Anna Kreshuk's normalDist.C

 
from ROOT import TF1, TCanvas, TSystem, TAxis, TLegend
from ROOT import kRed, kGreen, kBlue
 
# Create the one dimensional 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()

Author

Juan Fernando Jaramillo Botero

Definition in file normalDist.py.