Poisson {distributions3} R Documentation

## Create a Poisson distribution

### Description

Poisson distributions are frequently used to model counts.

### Usage

Poisson(lambda)


### Arguments

 lambda The shape parameter, which is also the mean and the variance of the distribution. Can be any positive number.

### Details

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 lambda = \lambda.

Support: \{0, 1, 2, 3, ...\}

Mean: \lambda

Variance: \lambda

Probability mass function (p.m.f):

 P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} 

Cumulative distribution function (c.d.f):

 P(X \le k) = e^{-\lambda} \sum_{i = 0}^{\lfloor k \rfloor} \frac{\lambda^i}{i!} 

Moment generating function (m.g.f):

 E(e^{tX}) = e^{\lambda (e^t - 1)} 

### Value

A Poisson object.

Other discrete distributions: Bernoulli(), Binomial(), Categorical(), Geometric(), HurdleNegativeBinomial(), HurdlePoisson(), HyperGeometric(), Multinomial(), NegativeBinomial(), ZINegativeBinomial(), ZIPoisson(), ZTNegativeBinomial(), ZTPoisson()

### Examples


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))


[Package distributions3 version 0.2.1 Index]