Poisson clumping

The Poisson process provides a description of random independent events occurring with uniform probability through time and/or space.

If λ is small, events are rare, but may nevertheless occur in clumps—referred to as Poisson clumps or bursts—purely by chance.

[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.

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.