ROOTR Notes

Basics on Statistical Analysis

Some notes on basic conceps and it tools in R and some examples on ROOTR

Distribution/pdf	Example use in HEP
Binomial	Branching ratio
Multinomial	Histogram with fixed N
Poisson	Number of events found
Uniform	Monte Carlo method
Exponential	Decay time
Gaussian	Measurement error
Chi-square	Goodness-of-fit
Cauchy	Mass of resonance
Landau	Ionization energy loss

http://www.pp.rhul.ac.uk/~cowan/stat_cern.html

erf(Error Function) and erf.inv (Inverse Error Function)

http://mathworld.wolfram.com/InverseErf.html

(For Gaussian Distribution)

erf <- function(x) 2 * pnorm(x * sqrt(2)) - 1 
erf.inv <- function(x) qnorm((x + 1)/2)/sqrt(2)

Example

erf.inv(1) 
erf.inv(0) 
erf.inv(-1) 
erf.inv(erf(.25)) 
erf(erf.inv(.25)) 
erf.inv(.5)

source link

KDE Kernel Density Estimation 1D

The way to get PDF ;D
Just use de function density(x)

PDF (Probability Density Function)

http://reference.wolfram.com/mathematica/ref/SmoothKernelDistribution.html

http://reference.wolfram.com/mathematica/ref/PDF.html

x <- log(rgamma(150,5))
PDF <- approxfun(density(x))
plot(density(x))
xnew <- c(0.45,1.84,2.3)
points(xnew,df(xnew),col=2)

source link

Multivariate Analysis Approach

KDE Kernel Density Estimation

Exist a package called ks that lets you to calculate a KDE and KDA
letting you to calculate an optimal h(bandwidth or smoothing) with full or diagonalized matrix.
paper at http://www.jstatsoft.org/v21/i07/paper

Autor: Omar Andres Zapata Mesa

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