| 词条 | Poisson clumping |
| 释义 |
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. EtymologyPoisson 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. HistoryThe 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] ApplicationsPoisson 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{{incomprehensible|section=yes|date=July 2016}}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 that have a specific monotonicity property for large exclusions. The probability that such a process will achieve a large value is asymptotically small and is distributed in a Poisson fashion.[6] See also
References1. ^1 {{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}} 2. ^{{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}} 3. ^{{cite web|url=http://www.stat.ualberta.ca/people/schmu/preprints/poisson.pdf|title=Shark attacks and the Poisson approximation|first=Byron|last=Schmuland}} 4. ^Anteneodo, C.; Malmgren, R. D.; Chialvo, D. R. (2010.) "Poissonian bursts in e-mail correspondence", The European Physical Journal B, 75(3):389–94. 5. ^Aldous, D. (1989.) "Probability Approximations via the Poisson Clumping Heuristic", Applied Mathematical Sciences, 7, Springer 6. ^Sethares, W. A. and Bucklew, J. A. (1991.) Exclusions of Adaptive Algorithms via the Poisson Clumping Heuristic, University of Wisconsin. 2 : Poisson point processes|Markov processes |
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