Poisson clumping, orPoisson bursts,^[1] is a phenomenon whererandom events may appear to occur in clusters, clumps, orbursts.

Poisson clumping is named for 19th-centuryFrench mathematicianSiméon Denis Poisson,^[1] known for his work ondefinite integrals,electromagnetic theory, andprobability theory, and after whom thePoisson distribution is also named.

ThePoisson 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. Thedistribution of the number of events follows aPoisson 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 caseWeibull 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 byDavid Aldous in 1989,^[7] is a model for findingfirst-order approximations over different areas in a large class ofstationary probability models. The probability models have a specificmonotonicity property with largeexclusions. The probability that this will achieve a large value isasymptotically small and is distributed in aPoisson fashion.^[8]

• Burstiness
• Clustering illusion
• Texas sharpshooter fallacy