Poisson

Poisson distribution

Derived by French Poisson

in 1837

Bortkiewicz(1898)

First application

By Bortkiewicz, 1898

Number of deaths by

Horse Kicking

In Prussian army

The LAW of Rare Events

Law is used as a synonym of probability distribution,

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

Proof of Law of Rare Events

Horse Kicking

Number of soldiers killed

by horse-kicks each year

in each corps

in Prussian cavalry.

# 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

Mu=mean # of occurrencesy=0, 1, 2, …

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

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

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