The Poisson Distribution

The Poisson distribution is a great tool for statisticians trying to predict how data will be distributed. In 1946, British statistician R.D. Clarke published a paper called “An Application of the Poisson Distribution” analyzing the distribution of flying bomb hits in London during World War II. The British military wanted information to determine if German missiles were targeting specific districts randomly or if they were targeting important installations randomly. If so, dispersing those important installations would decrease their chance of being hit.

A Poisson distribution occurs in several important situations. One is that it approximates the binomial distribution in many situations. Each interval t is independent from the next so the probability that an individual will succeed within it roughly proportional to Dt. The probability of one event occurring in any given time interval is much lower than the probability that several of the same events will occur. The Poisson distribution can be used as an approximate binomial distribution.

Poisson distributions are useful in many fields. It can be used by businessmen to predict the likelihood of an event within a given time period. The Poisson distribution in biology can be used to predict how many offspring survive a mutation over a time period. Scientists can use it in a laboratory to estimate the number offspring in a genetic pool. This can be used to forecast the health of the population.

The Poisson Distribution
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