Create a Poisson distribution
Poisson distributions are frequently used to model counts.
Poisson(lambda)
lambda |
The shape parameter, which is also the mean and the variance of the distribution. Can be any positive number. |
We recommend reading this documentation on https://alexpghayes.github.io/distributions3, where the math will render with additional detail.
In the following, let X be a Poisson random variable with parameter
lamdba = 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))
A Poisson object.
Other discrete distributions: Bernoulli,
Binomial, Categorical,
Geometric, HyperGeometric,
Multinomial, NegativeBinomial
set.seed(27) X <- Poisson(2) X random(X, 10) pdf(X, 2) log_pdf(X, 2) cdf(X, 4) quantile(X, 0.7) cdf(X, quantile(X, 0.7)) quantile(X, cdf(X, 7))
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