# Landau Distribution: Definition, Parameters

The Landau distribution is a unimodal distribution with a long upper tail; It resembles a normal distribution (called a Gaussian distribution in physics). This distribution has fat tails, which decrease algebraically (as opposed to exponentially) for large values of x. It is defined over the set of real numbers

In physics, the Landau Distribution describes fluctuations in energy loss of a charged particle passing through a medium, like a thin layer of material. The long tail is because of large fluctuations in high energy ionization.

## Landau Distribution Mean and Variance

The mean and variance are not defined for this distribution.

## Location and Scale Parameters

The distribution’s overall shape is determined by:

• The location parameter (μ), which tells you where on the horizontal axis a graph is centered, relative to the standard normal model.
• The scale parameter (δ) stretches or squeezes the graph.

## References

Egede, U. (1998). Ionisation from charged particles.
Retrieved October 8, 2019 from: http://www.hep.lu.se/atlas/thesis/egede/thesis-node36.html
Gilmore, R. (1992). Single Particle Detection And Measurement. CRC Press.
Reygers, K. & Neubert, S. (2017-2018)Statistical Methods in Particle Physics 2. Probability Distributions. Retrieved OCtober 8, 2019 from:
https://www.physi.uni-heidelberg.de/~reygers/lectures/2017/smipp/stat_methods_ss2017_02_distributions.pdf
Meroli, S. The Landau distribution for ionizing particles. Retrieved October 8, 2019 from:
meroli.web.cern.ch › Lecture_landau_ionizing_particle