Poisson distribution
Poisson Distribution
The Poisson Distribution (pronounced pwa-son) is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.
Etymology
The Poisson Distribution is named after French mathematician Siméon Denis Poisson, who introduced this distribution in his work "Recherches sur la Probabilité des Jugements en Matière Criminelle et en Matière Civile" ("Research on the Probability of Judgments in Criminal and Civil Matters"), published in 1837.
Definition
The probability mass function of a Poisson Distribution is given by:
- P(k events in interval) = λ^k * e^-λ / k!
where:
- λ is the average rate of value (also called the rate parameter)
- k is the actual number of events
- e is the base of the natural logarithm (approximately equal to 2.71828)
- k! is the factorial of k
Related Terms
- Probability Distribution: A mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
- Siméon Denis Poisson: A French mathematician, geometer, and physicist who made many scientific contributions and is known for the Poisson Distribution.
- Rate Parameter: A parameter of a model, usually a positive real number, that determines the relative rate at which events occur.
- Factorial: The product of an integer and all the integers below it, denoted by k!.
Applications
The Poisson Distribution is used in various fields such as mathematics, statistics, engineering, and physics. It is particularly useful in medical research for modeling the number of times an event occurs within a specific time period. For example, it can be used to model the number of patients arriving in an emergency room within a given time period, or the number of cells infected by a virus in a certain volume.
External links
- Medical encyclopedia article on Poisson distribution
- Wikipedia's article - Poisson distribution
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