Poisson clumping, or Poisson bursts,[1] is a phenomenon where random events may appear to occur in clusters, clumps, or bursts.
Poisson clumping, or Poisson bursts,[1] is a phenomenon where random events may appear to occur in clusters, clumps, or bursts.
Poisson clumping is named for 19th-century French mathematician Siméon Denis Poisson,[1] known for his work on definite integrals, electromagnetic theory, and probability theory, and after whom the Poisson distribution is also named.
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.[2] In many cases there is no other cause behind such indefinite groupings besides the nature of randomness following this distribution.[3] 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.[4]
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.[5][6]
The poisson clumping heuristic (PCH), published by David Aldous in 1989,[7] 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.[8]