Definition

Noun: A Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, provided these events occur with a known constant mean rate and independently of the time since the last event.

Usage

The Poisson distribution is used to model the probability of rare, independent events over a specified interval. * The number of calls received by a call center per hour can be modeled using a Poisson distribution. * Scientists used the Poisson distribution to predict the probability of a specific number of radioactive decays in a given time period.

Advanced Usage

• As an approximation: The Poisson distribution is often used as an approximation to the binomial distribution when the number of trials (n) is large and the probability of success (p) is small.
  • For modeling rare manufacturing defects in a large batch of products, the Poisson distribution serves as an excellent approximation.

Variants and Related Words

• Poisson (adjective): Pertaining to or following the Poisson distribution.
  • The data exhibited Poisson characteristics.
• Distribution (noun): In statistics, a function that shows the possible values for a variable and how often they occur.

Synonyms

• Poisson law

Related Phrases and Concepts

• Poisson process: A stochastic process that counts the number of events and the times at which these events occur in a given time interval, where the events follow a Poisson distribution.
  • The arrival of customers is often modeled as a Poisson process.
• Lambda (λ): The parameter of a Poisson distribution, representing the expected number of occurrences in the given interval.
  • The key parameter for the Poisson distribution is lambda (λ), the average rate.

Noun

1. a theoretical distribution that is a good approximation to the binomial distribution when the probability is small and the number of trials is large