(1.5 hours to learn)
The Poisson distribution is a discrete probability distribution for the counts of independent random events in a given time interval, e.g. babies born in a hospital in 1 month or lightening strikes in Mexico in 1 week. It is one of the most common discrete distributions used in virtually every scientific and financial field.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ Khan Academy: Probability and Statistics
Location: lecture sequence "poisson processes"
→ A First Course in Probability
An introductory probability textbook.
Location: Section 4.7, "The poisson random variable," pages 160-173
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 2.1.5, "The Poisson distribution," pages 42-47
→ Mathematical Methods in the Physical Sciences
Location: Ch 13.9 (p 728)
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: 5.4 (p 287)
Supplemental resources (the following are optional, but you may find them useful)
→ Mathematical Monk: Probability Primer (2011)
Online videos on probability theory.
Location: Article: Poisson Distribution
→ Wolfram MathWorld
- Poisson processes are a kind of stochastic process where counts of events within a set follow a Poisson distribution.
- For large values of the scale parameter, the Poisson distribution is well approximated by a Gaussian distribution. This follows from the Central Limit Theorem .
- The Poisson distribution is a member of the exponential family .
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