Poisson Distribution - Occurrence

Occurrence

Applications of the Poisson distribution can be found in many fields related to counting:

• Electrical system example: telephone calls arriving in a system.
• Astronomy example: photons arriving at a telescope.
• Biology example: the number of mutations on a strand of DNA per unit length.
• Management example: customers arriving at a counter or call centre.
• Civil Engineering example: cars arriving at a traffic light.
• Finance and Insurance example: Number of Losses/Claims occurring in a given period of Time.
• Earthquake Seismology example: An asymptotic Poisson model of seismic risk for large earthquakes. (Lomnitz, 1994).

The Poisson distribution arises in connection with Poisson processes. It applies to various phenomena of discrete properties (that is, those that may happen 0, 1, 2, 3, ... times during a given period of time or in a given area) whenever the probability of the phenomenon happening is constant in time or space. Examples of events that may be modelled as a Poisson distribution include:

• The number of soldiers killed by horse-kicks each year in each corps in the Prussian cavalry. This example was made famous by a book of Ladislaus Josephovich Bortkiewicz (1868–1931).
• The number of yeast cells used when brewing Guinness beer. This example was made famous by William Sealy Gosset (1876–1937).
• The number of phone calls arriving at a call centre per minute.
• The number of goals in sports involving two competing teams.
• The number of deaths per year in a given age group.
• The number of jumps in a stock price in a given time interval.
• Under an assumption of homogeneity, the number of times a web server is accessed per minute.
• The number of mutations in a given stretch of DNA after a certain amount of radiation.
• The proportion of cells that will be infected at a given multiplicity of infection.