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The Poisson distribution is a discrete probability distribution that is often used for a model distribution of count data, such as the number of traffic accidents and the number of phone calls received within a given time period. This entry begins with a definition and description of the properties of the Poisson distribution, which is followed by a discussion of how the Poisson distribution is obtained or estimated. Finally, this entry presents a discussion of applications for the distribution and its history.

Definition and Properties

The Poisson distribution is specified by a single parameter μ which determines the average number of occurrences of an event and takes any positive real number (i.e., μ >0). When a random variable X, which can take all nonnegative integers (i.e., X ...

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