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Discrete probability distribution modeling counts of independent events in a fixed interval at a constant average rate.
DESCRIPTION
The Poisson distribution models event counts with parameter λ equal to both mean and variance. It arises from the Poisson process where events occur independently at a constant rate. Applications include call arrivals, defects, and rare events. Overdispersion suggests alternatives like negative binomial. In GLMs, Poisson is used with a log link for count regression. Assumptions include independence and constant rate within the interval.
ALTERNATIVE DEFINITIONS
Encyclopaedia Britannica
Poisson distribution, in statistics, a distribution that expresses the probability of a given number of events occurring in a fixed time or space.
Highlights fixed time or space intervals for event counts.
NIST/SEMATECH e-Handbook
The Poisson distribution is used for modeling the number of events that occur in an interval of time or space.
Focuses on modeling counts per interval with examples.
Khan Academy
The Poisson distribution is used to model counts of events occurring within a fixed interval of time or space.
Educational framing with simple, accessible language.
RELATED TERMS
Poisson Process Exponential Distribution Rate Parameter Count Data Variance Negative Binomial GLM Overdispersion
COMPETING TERMS
Binomial Distribution Negative Binomial Distribution
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist Data Analyst AI Engineer
EXTERNAL SOURCES
- Wikipedia - Poisson distribution
- NIST - NIST overview of Poisson
- Khan Academy - Poisson distribution tutorial
- Wolfram MathWorld - Mathematical properties reference
TOP QUESTIONS
When should the Poisson Distribution be applied?
Use it for independent event counts in fixed intervals with a constant average rate, such as calls per hour.
Category: Requirements
What is a hot topic around Poisson Distribution?
Handling overdispersion in count data using negative binomial models or quasi-Poisson GLMs.
Category: Topic
What are common mistakes with Poisson Distribution?
Assuming independence or constant rate when data exhibits seasonality, clustering, or varying exposure.
Category: Mistakes
How is Poisson Distribution parameterized?
It is parameterized by λ (lambda), which equals both the mean and the variance.
Category: Definition
How does Poisson Distribution relate to Poisson Process?
Counts in a Poisson process over an interval follow a Poisson distribution with parameter proportional to the interval length.
Category: Example
What is the risk of misusing Poisson Distribution?
Model misspecification yields biased inferences; consider alternative count models when assumptions fail.
Category: Risk
How is Poisson used in regression?
In GLMs with a log link, Poisson models counts as a function of covariates, often with offsets for exposure.
Category: Definition
Why is Poisson Distribution still relevant?
It underpins many count models and is simple to fit and interpret in practice.
Category: Relevancy
What diagnostic indicates overdispersion?
Variance substantially exceeding the mean suggests overdispersion; residual analysis and dispersion tests help confirm.
Category: Testing