# Talk:Landau distribution

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It should be noted that the Landau distribution has no free parameters! Thus, the curve in the figure is wrong. There is no Landau distribution with a most probable value of 2 and a ${\displaystyle \sigma }$ of 1. Actually the most probable value is (ROOT TMath::Landau()) around 0.222.
Just by scaling and shifting one can introduce artificially a most probable value and a width

${\displaystyle x\rightarrow {\frac {x-MPV}{\sigma }}-0.222}$

## The physics of high energy ionized particles going through a thin piece of material

Deserves its own page too, and link back and forth.82.171.225.84 (talk) 21:09, 16 August 2011 (UTC)

## Derivation

Could someone who knows add a section on why this is the distribution of particles' energy loss travelling through a thin medium?

## Approximate expression wrong?

Is there a mistake in the approximation given? (which is used for the figure).

${\displaystyle p(x)={\frac {1}{\sqrt {2\pi }}}\exp \left\{-{\frac {1}{2}}(x+e^{-x})\right\}.}$

This has a peak at x=-0.001 p=0.242. Whereas the integral (evaluated with scipy)

${\displaystyle p(x)={\frac {1}{\pi }}\int _{0}^{\infty }\!e^{-t\log t-xt}\sin(\pi t)\,dt.}$

give a peak at x=-0.223, p=0.181 which agrees with GSL:

#!/usr/bin/env python
import numpy
from matplotlib import pyplot
import pygsl.rng
x = numpy.linspace(-4, 10, 1000)
pyplot.plot(x, pygsl.rng.landau_pdf(x))
pyplot.show()


195.194.110.142 (talk) 14:15, 13 January 2015 (UTC)