Pois-class {distr}R Documentation

Class "Pois"

Description

The Poisson distribution has density

p(x) = lambda^x exp(-lambda)/x!

for x = 0, 1, 2, .... The mean and variance are E(X) = Var(X) = λ.

C.f. rpois

Objects from the Class

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

Slots

img:
Object of class "Naturals": The space of the image of this distribution has got dimension 1 and the name "Natural Space".
param:
Object of class "PoisParameter": the parameter of this distribution (lambda), declared at its instantiation
r:
Object of class "function": generates random numbers (calls function rpois)
d:
Object of class "function": density function (calls function dpois)
p:
Object of class "function": cumulative function (calls function ppois)
q:
Object of class "function": inverse of the cumulative function (calls function qpois). The quantile is defined as the smallest value x such that F(x) >= p, where F is the distribution function.
support:
Object of class "numeric": a (sorted) vector containing the support of the discrete density function
.withArith:
logical: used internally to issue warnings as to interpretation of arithmetics
.withSim:
logical: used internally to issue warnings as to accuracy
.logExact:
logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExact:
logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

Extends

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

Methods

+
signature(e1 = "Pois", e2 = "Pois"): For the Poisson distribution the exact convolution formula is implemented thereby improving the general numerical approximation.
initialize
signature(.Object = "Pois"): initialize method
lambda
signature(object = "Pois"): returns the slot lambda of the parameter of the distribution
lambda<-
signature(object = "Pois"): modifies the slot lambda of the parameter of the distribution

Note

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

Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de

See Also

PoisParameter-class DiscreteDistribution-class Naturals-class rpois

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).

[Package distr version 2.1.3 Index]