Talk:Landau distribution

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 $\sigma$ 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

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

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).

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

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

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

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)

When I plotted the second approximation vs GSL, it appears to look only vaguely like the Landau distribution and has the wrong tail behaviour. The tail isn't even a power law, so it can't be correct just by inspection. Skewray (talk) 17:49, 29 July 2023 (UTC)

Figure

The figure should show the parameter values used.

--Scharleb (talk) 19:05, 9 December 2021 (UTC)

This appears to have been fixed, although the approximation figure may have other issues. Skewray (talk) 19:26, 29 July 2023 (UTC)

Properties Section

The properties section is unnecessary. All those properties follow from the Landau distributions being stable. Skewray (talk) 19:25, 29 July 2023 (UTC)

Wrong μ?

I have to set μ = π/2 log (π/2) in order to get the Landau distribution to match the parametrization given for stable distributions in the stable distributions article. Does this article use a different stable distribution parametrization? There are at least ten in use... Skewray (talk) 15:50, 4 October 2023 (UTC)