# Poisson

```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
/yr/corps
0
1
2
3
4
5+
Total
Obs’ed
Freq.
109
65
22
3
1
0
200
Poisson exp’ed
Freq.
108.7
66.3
20.2
4.1
0.6
0.1
200.0
Mu=mean # of occurrences
y=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