Pois-class {distr} | R Documentation |
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 can be created by calls of the form Pois(lambda)
.
This object is a Poisson distribution.
img
:"Naturals"
:
The space of the image of this distribution has got dimension 1
and the name "Natural Space".param
:"PoisParameter"
:
the parameter of this distribution (lambda), declared at its
instantiationr
:"function"
:
generates random numbers (calls function rpois)d
:"function"
:
density function (calls function dpois)p
:"function"
:
cumulative function (calls function ppois)q
:"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
:"numeric"
: a (sorted)
vector containing the support of the discrete density function
Class "DiscreteDistribution"
, directly.
Class "UnivariateDistribution"
, by class "DiscreteDistribution"
.
Class "Distribution"
, by class "DiscreteDistribution"
.
signature(e1 = "Pois", e2 = "Pois")
:
For the Poisson distribution the exact convolution formula is
implemented thereby improving the general numerical approximation.signature(.Object = "Pois")
:
initialize methodsignature(object = "Pois")
:
returns the slot lambda of the parameter of the distributionsignature(object = "Pois")
:
modifies the slot lambda of the parameter of the distribution
Working with a computer, we use a finite interval as support which carries at least mass 1-getdistrOption("TruncQuantile")
.
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de
PoisParameter-class
DiscreteDistribution-class
Naturals-class
rpois
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).