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(external link)

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

http://mathworld.wolfram.com/InverseErf.html(external link) (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(external 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(external link)
http://reference.wolfram.com/mathematica/ref/PDF.html(external link)
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(external 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(external link)




Autor: Omar Andres Zapata Mesa


El documento original está disponible en https://clustercien.udea.edu.co/web/tiki-index.php?page=ROOTR+Notes