# Sigma of Landau distribution

Dear All,

I needed to estimate a width of some signal and I used Landau distribution to fit this signal. However, now I am missing exact interpretation of what is “sigma”? At least what is the ratio “sigma” <-> FWHM? looking in CERNLIB denlan function and information about Landau distribution did not make it clear. Can anybody help with it?
Thank you.

Hi!

Just after 6 years…an answer for you! (well, I’m new in this forum…and unfortunately we live in 2011!).
In ROOT the Landau distribution has got two parameters, the MPV (most probable value) and another not well defined ‘SIGMA’.
But you can see the Particle Data Group (PDG) here:

http://pdg.lbl.gov/2010/reviews/contents_sports.html

in the

Experimental Methods and Collider > Passage of particles through matter (rev.) > Fluctuations in energy loss

section. In particular, the MPV is the mean value of Bethe-Bloch energy loss, and the 'Landau width’
is w = 4csi where csi = (K/2)(Z/A)*(x/beta^2) with K = 0.307 MeV / (g cm^2) and a thickness x in g/(cm^2).

So, you can take SIGMA = w (the FWHM of the curve).

In the code for instance you can use the TF1 class:

``````TF1 *landauDistr = new TF1("landauDistr","TMath::Landau(x,[0],[1])",Emin,Emax);
landauDistr->SetParameter(0,mpv);
landauDistr->SetParameter(1,w);``````

implementing a Double_t mpv and Double_t w as PDG.

Sorry, I know that my answer is useless after 6 years. But perhaps we can report to ROOT developers
the poor documentation about the Landau parameters!

Bye
luca

Hi!

So, to sum up, FWHM of Landau distribution = 4*sigma, where sigma is what ROOT writes under “MPV” line in terminal or in Statbox.

Hi,
Can anyone please clarify if we need to pass mpv or the (truncated) mean of the landau distribution to generate the random numbers? In this link http://www.slac.stanford.edu/comp/unix/package/cernroot/22309/TRandom.html#TRandom:Landau they write the first argument as “mean”.

-Regards,
Kolahal

Hi,

The mean to pass in TRandom::Landau is the location parameter of the distribution and not the most probable value (the mode) of the distribution. The sigma is instead a scale parameter.