Talk:Landau distribution

Latest comment: 1 year ago by Skewray in topic Wrong μ?

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 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

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

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

Derivation

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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?

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

 

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

 

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)Reply

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)Reply

Figure

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The figure should show the parameter values used.

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

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

Properties Section

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

Wrong μ?

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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)Reply