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Understanding the Poisson Distribution

Achim Zeileis shows off my favorite statistical distribution:

The Poisson distribution has many distinctive features, e.g., both its expectation and variance are equal and given by the parameter λλ. Thus, E(Y)=λE(Y)=λ and Var(Y)=λVar(Y)=λ. Moreover, the Poisson distribution is related to other basic probability distributions. Namely, it can be obtained as the limit of the binomial distribution when the number of attempts is high and the success probability low. Or the Poisson distribution can be approximated by a normal distribution when λλ is large. See Wikipedia (2002) for further properties and references.

Here, we leverage the distributions3 package (Hayes et al. 2022) to work with the Poisson distribution in R. In distributions3, Poisson distribution objects can be generated with the Poisson() function. Subsequently, methods for generic functions can be used print the objects; extract mean and variance; evaluate density, cumulative distribution, or quantile function; or simulate random samples.

Read on for a detailed tutorial. H/T R-bloggers.

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