Poisson
The Poisson Distribution

### Description

Calculates density, cumulative probability, quantile, and generate random sample for the Poisson distribution (discrete).

### Usage

    dpois(x, lambda, log = FALSE) # density
    ppois(q, lambda, lower.tail = TRUE, log.p = FALSE) # probability
    qpois(p, lambda, lower.tail = TRUE, log.p = FALSE) # quantile
    rpois(n, lambda) # random

### Arguments

x, q | numeric vectors in the range [0, Inf) that specify the quantiles.
p | a numeric vector in the range [0, 1] that specifies the probabilities.
n | an integer value in the range [0, Inf) that specifies the number of random samples requested. If the input value is not an integer, it is truncated. If length(n) is greater than 1, the random function returns length(n) random samples.
lambda | a numeric vector in the range [0, Inf) that specifies the means.
log | a logical value. If FALSE (default), the density function returns the density itself. If TRUE, it returns the log of the density.
lower.tail | a logical value. If TRUE (default), the probability supplied to the quantile function or returned by the probability function is P[X <= x]. If FALSE, it is P[X > x].
log.p | a logical value. If FALSE (default), the probability supplied to the quantile function or returned by the probability function is the probability itself. If TRUE, it is the log of the probability.

### Details

The distribution parameter(s) are replicated cyclically to be the same length as the input x, q, p, or the number of random samples requested.
Missing values (NAs) in the input or the distribution parameter(s) will cause the corresponding elements of the result to be missing.
Value
returns density (dpois), cumulative probability (ppois), quantile (qpois), or random sample (rpois) for the Poisson distribution with parameter lambda. The quantile is defined as the smallest value q such that Pr(Poisson random variate <= x) >= p.
Side Effects
If the .Random.seed dataset exists, the random sample function updates its value. The random sample function creates the .Random.seed dataset if it does not exist.
Background
The Poisson distribution is the discrete probability distribution of the number of events occurring in a fixed period of time if these events occur with a known average rate lamda and independently of the time since the last event. It has support on the set {0, 1, 2, 3, …}.
See Also
set.seed, Binomial
Examples

    rpois(20,3)  #sample of size 20 with a mean of 3

Package stats version 6.1.5-18
Package Index