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dist_poisson
The Poisson Distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_poisson(lambda)
Arguments
lambda |
vector of (non-negative) means. |
Details
Poisson distributions are frequently used to model counts.
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let X be a Poisson random variable with parameter
lambda = λ.
Support: {0, 1, 2, 3, ...}
Mean: λ
Variance: λ
Probability mass function (p.m.f):
P(X = k) = λ^k e^(-λ) / k!
Cumulative distribution function (c.d.f):
P(X ≤ k) = e^(-λ) ∑_{i = 0}^k λ^i / i!
Moment generating function (m.g.f):
E(e^(tX)) = e^(λ (e^t - 1))
See Also
Examples
dist <- dist_poisson(lambda = c(1, 4, 10)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7)