< List of probability distributions < Argus distribution
The Argus distribution is a continuous probability distribution introduced by the ARGUS collaboration (A Russian-German-United States-Swedish Collaboration), which investigated f-mesons at Germany’s electron-positron collider ring DORIS II in the late 80s and early 90s [1]. The distribution is especially suited to modeling cases in physics of combinatorial backgrounds with sharp-edged kinematical bounds [2].
Properties of the Argus distribution
The probability density function (pdf) for the ARGUS distribution is [4]:
where:
-
- c and χ are the distribution’s parameters with 0 < x < c and χ > 0,
- Ψ(χ) = Φ(χ) – (χ)φ (χ) – ½,
- where Φ(χ) is the cumulative distribution function (CDF) of the standard normal distribution and
- φ (χ) is the pdf of the standard normal distribution.
Uses for the Argus distribution
The Argus distribution has a hard cutoff at x =1, making it a good option for modeling scenarios with sharp boundaries in the data. For instance, it has been applied to the modeling of the invariant mass of hadronic jets in particle physics, wherein a minimum mass defines the jets [5].
This distribution is also useful in representing combinatorial backgrounds in particle physics. These backgrounds arise from random particle combinations and often display sharp edges in their distributions. By using the Argus distribution to model these sharp edges, the accuracy of background estimation can be enhanced.
The unrelated P.Argus distribution
The choice of the name “Argus” for this distribution is somewhat unfortunate as a search of the literature will bring up many unrelated hits from sources as diverse as marine biology and historical oil holdings!
For example, some researchers have studied the Panulirus argus (or P.Argus) — the Caribbean spiny lobster. This species of spiny lobster lives on reefs and in mangrove swamps in the western Atlantic Ocean and its spread can be modeled with a “P.Argus” distribution — completely unrelated to the Argus distribution used in physics.
Another completely unrelated search entry pertains to the Argus Natural Gas Company, which was eventually consolidated with Enron.
“Not content with this state of affairs, Northern, Peoples,
From Ritchie’s Integration of Public Utility Holding Companies, 1954, p.128
and Argus sought permission to retain the Argus distribution
properties within Northern’s integrated system”
References
[1] ARGUS collaboration. Albrecht, H. et al. Search for hadronic b->u decays. Phys. Lett. B241, 278-282 (1990) 3.
[2] Lista, L. (2017). Statistical Methods for Data Analysis in Particle Physics. Springer.
[3] Image: Shiyu Ji, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons
[4] Clustering package (scipy.cluster) scipy.stats.argus# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.argus.html
[5] Physics with ARGUS. Retrieved August 17, 2023 from: https://bib-pubdb1.desy.de/record/491246/files/desy96-015.pdf