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

Symmetry

object of class "DistributionSymmetry"; used internally to avoid unnecessary calculations.

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@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de

See Also

PoisParameter-class DiscreteDistribution-class Naturals-class rpois

Examples

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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).

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