Friday, November 30, 2012

Poisson Distribution Facts - Some Really Interesting Stuff

The Poisson Distribution is a probability distribution.  A probability distribution assigns the probability of an event occurring in a random experiment.  In fact, it assigns the probability of every possible event occurring.  That's what makes it a distribution.

Understanding probability distributions empowers us to estimate how likely an event is to occur.   Different distribution models fit different types of data.  In 1898, Ladislaus Bortkiewicz published the book The Law of Small Numbers.  He discussed an interesting question, "How many Prussian cavalrymen are killed by horse kicks."

You may have no interest in the number of deaths per horse kick per year in a cavalry, but you probably do have your own questions.  You can use a Poisson probability distribution model if your data meets these criteria:

1.  The likelihood of the event you want to measure is small (thus the title "The Law of Small Numbers").
2.  The events of interest are independent.  For instance, when you flip a coin more than once, the second toss does not depend on the outcome of the first toss.
3.  The event can be counted in whole numbers, like how many times a salesman rings your doorbell.
4.  You would not ask how many times something did not happen, like how many times a salesman did not ring your doorbell.

The first step in constructing a Poisson distribution is to collect data and determine how often the event really does occur in the data.  But that is a topic for another day.

Don't be afraid to ask questions and construct your own data sets!

Happy experimenting.

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