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Diving Into the Poisson Distribution and Poisson Process
What role does the Poisson distribution and Poisson process take in probability and statistics, and how is it used in real-life scenarios?
Author(s): Saniya Parveez, Roberto Iriondo
In this article, we will dive into the Poisson process and Poisson distribution. We will showcase some relevant statistical concepts, followed by real-world case scenarios and examples with a Python implementation. Make sure to check the entire implementation from this tutorial on either Google Colab or Github.
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The Poisson distribution is alternatively derived from a binomial distribution. It is a probability distribution used in statistical-related work, used in situations where the probability of an event happening is rare. Therefore, distribution is used to describe the behavior of rare events [1].
Many experimental situations occur when we observe the count of events within a set of time, area, length, and so on. It is a discrete probability distribution, and it is widely used in statistical work. It is used in those situations where the probability of an event is small, i.e., the event rarely occurs [2].
The Poisson distribution came to its inception after the French mathematician Siméon Poisson in 1837 and the first application was the description of the number of deaths by horse kicking in the Prussian army [11].
The Equation of Poisson distribution can be described as:
