|WikiProject Statistics||(Rated Start-class, Low-importance)|
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
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).
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()