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)
 * $$p(x) = \frac{1}{\pi} \int_0^\infty\! e^{-t \log t - x t} \sin(\pi t)\, dt.$$

give a peak at x=-0.223, p=0.181 which agrees with GSL: 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)
 * 1) !/usr/bin/env python


 * 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)