Poisson clumping
Poisson clumping, or Poisson bursts,[1] is the phenomenon wherein random events may appear to have a tendency to occur in clusters, clumps, or bursts.
Etymology[]
Poisson clumping is named for the 19th-century French mathematician Siméon Denis Poisson,[1] who is known for his work on definite integrals, electromagnetic theory, and probability theory and is the namesake of the Poisson distribution.
History[]
The Poisson process provides a description of random independent events occurring with uniform probability through time or space (or both). 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 purely by chance they may, nevertheless, occasionally occur in clusters, also referred to as Poisson clumps or Poisson bursts.[2]
Applications[]
Poisson clumping is used to explain marked increases or decreases in the frequency of an event, such as shark attacks, "coincidences", birthdays, or heads or tails from coin tosses, and e-mail correspondence.[3][4]
Poisson clumping heuristic[]
The poisson clumping heuristic (PCH), published by David Aldous in 1989,[5] 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.[6]
See also[]
References[]
- ^ a b Yang, Jennifer (30 January 2010). "Numbers don't always tell the whole story". Toronto Star.
- ^ "Shark Attacks May Be a "Poisson Burst"". Science Daily. 23 August 2011.
- ^ Schmuland, Byron. "Shark attacks and the Poisson approximation" (PDF).
- ^ Anteneodo, C.; Malmgren, R. D.; Chialvo, D. R. (2010.) "Poissonian bursts in e-mail correspondence", The European Physical Journal B, 75(3):389–94.
- ^ Aldous, D. (1989.) "Probability Approximations via the Poisson Clumping Heuristic", Applied Mathematical Sciences, 7, Springer
- ^ Sethares, W. A. and Bucklew, J. A. (1991.) Exclusions of Adaptive Algorithms via the Poisson Clumping Heuristic, University of Wisconsin.
- Poisson point processes
- Markov processes