Pois-class

0th

Percentile

Class "Pois"

The Poisson distribution has density $$p(x) = \frac{\lambda^x e^{-\lambda}}{x!}$$ for $x = 0, 1, 2, \ldots$. The mean and variance are $E(X) = Var(X) = \lambda$. C.f. rpois

Keywords
distribution
Note

Working with a computer, we use a finite interval as support which carries at least mass 1-getdistrOption("TruncQuantile").

Objects from the Class

Objects can be created by calls of the form Pois(lambda). This object is a Poisson distribution.

Extends

Class "DiscreteDistribution", directly. Class "UnivariateDistribution", by class "DiscreteDistribution". Class "Distribution", by class "DiscreteDistribution".

concept

  • discrete distribution
  • lattice distribution
  • Poisson distribution
  • S4 parameter class
  • generating function

See Also

PoisParameter-class DiscreteDistribution-class Naturals-class rpois

Aliases
  • Pois-class
  • Pois
  • initialize,Pois-method
Examples
P <- Pois(lambda = 1) # P is a Poisson distribution with lambda = 1.
r(P)(1) # one random number generated from this distribution, e.g. 1
d(P)(1) # Density of this distribution is 0.3678794 for x = 1.
p(P)(0.4) # Probability that x < 0.4 is 0.3678794.
q(P)(.1) # x = 0 is the smallest value x such that p(B)(x) >= 0.1.
lambda(P) # lambda of this distribution is 1.
lambda(P) <- 2 # lambda of this distribution is now 2.
R <- Pois(lambda = 3) # R is a Poisson distribution with lambda = 2.
S <- P + R # R is a Poisson distribution with lambda = 5(=2+3).
Documentation reproduced from package distr, version 2.3.1, License: LGPL-3

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