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Poisson

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Poisson

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  1. Poisson

  2. Poisson distribution Derived by French Poisson in 1837

  3. Bortkiewicz(1898)

  4. First application By Bortkiewicz, 1898 Number of deaths by Horse Kicking In Prussian army

  5. The LAW of Rare Events Law is used as a synonym of probability distribution,

  6. Law of small numbers The distribution of # of occurrences of an event that happens RARELY but has very many opportunities to happen follows Poisson Distribution

  7. Proof of Law of Rare Events

  8. Horse Kicking Number of soldiers killed by horse-kicks each year in each corps in Prussian cavalry.

  9. # of men killed Obs’ed Poisson exp’ed /yr/corps Freq. Freq. 0 109 108.7 1 65 66.3 2 22 20.2 3 3 4.1 4 1 0.6 5+ 0 0.1 Total 200 200.0

  10. Mu=mean # of occurrencesy=0, 1, 2, …

  11. Examples of Applications • Mortality of infants in a city • # of misprints in a book • # of bacteria on a plate • # of activations of a Geiger counter • # of cars that pass through a certain point on a road during a given period of time

  12. Examples of Applications • # of phone calls at a call center per minute • # of times a web server is accessed per minute • # of spelling mistakes a secretary makes while typing a single page

  13. Examples of Applications • # of bombs falling on each unit area of London during a German air raid in the early part of WII • # of road-kill found per unit length of road • # of ((genetics) any event that changes genetic structure