Poisson clumping
Poisson clumping, or Poisson bursts,{{cite web|url=https://www.thestar.com/news/gta/2010/01/30/numbers_dont_always_tell_the_whole_story.html|title=Numbers don't always tell the whole story|first=Jennifer|last=Yang|work=Toronto Star|date=30 January 2010}} is a phenomenon where random events may appear to occur in clusters, clumps, or bursts.
Etymology
Poisson clumping is named for 19th-century French mathematician Siméon Denis Poisson, known for his work on definite integrals, electromagnetic theory, and probability theory, and after whom the Poisson distribution is also named.
History
The Poisson process provides a description of random independent events occurring with uniform probability through time and/or space. The expected number λ of events in a time interval or area of a given measure is proportional to that measure. The distribution of the number of events follows a Poisson distribution entirely determined by the parameter λ. If λ is small, events are rare, but may nevertheless occur in clumps—referred to as Poisson clumps or bursts—purely by chance.{{cite web|url=https://www.sciencedaily.com/releases/2001/08/010823084028.htm|title=Shark Attacks May Be a "Poisson Burst"|publisher=Science Daily|date=23 August 2011}} In many cases there is no other cause behind such indefinite groupings besides the nature of randomness following this distribution.Laurent Hodges, 2 - Common Univariate Distributions, in: Methods in Experimental Physics, v. 28, 1994, p. 35-61 However, obviously not all clumping in nature can be explained by this property — for example earthquakes, because of local seismic activity that causes groups of local aftershocks, in this case Weibull distribution is proposed.Min-Hao Wu, J.P. Wang, Kai-Wen Ku; Earthquake, Poisson and Weibull distributions, Physica A: Statistical Mechanics and its Applications, Volume 526, 2019, https://doi.org/10.1016/j.physa.2019.04.237.
Applications
Poisson clumping is used to explain marked increases or decreases in the frequency of an event, such as shark attacks, "coincidences", birthdays, heads or tails from coin tosses, and e-mail correspondence.{{cite web|url=http://www.stat.ualberta.ca/people/schmu/preprints/poisson.pdf|title=Shark attacks and the Poisson approximation|first=Byron|last=Schmuland}}Anteneodo, C.; Malmgren, R. D.; Chialvo, D. R. (2010.) "Poissonian bursts in e-mail correspondence", The European Physical Journal B, 75(3):389–94.
=Poisson clumping heuristic=
The poisson clumping heuristic (PCH), published by David Aldous in 1989,Aldous, D. (1989.) "Probability Approximations via the Poisson Clumping Heuristic", Applied Mathematical Sciences, 7, Springer is a model for finding first-order approximations over different areas in a large class of stationary probability models. The probability models have a specific monotonicity property with large exclusions. The probability that this will achieve a large value is asymptotically small and is distributed in a Poisson fashion.Sethares, W. A. and Bucklew, J. A. (1991.) Exclusions of Adaptive Algorithms via the Poisson Clumping Heuristic, University of Wisconsin.