Class "Pois"
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.
imgObject of class "Naturals":
The space of the image of this distribution has got dimension 1
and the name "Natural Space".
paramObject of class "PoisParameter":
the parameter of this distribution (lambda), declared at its
instantiation
rObject of class "function":
generates random numbers (calls function rpois)
dObject of class "function":
density function (calls function dpois)
pObject of class "function":
cumulative function (calls function ppois)
qObject 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.
supportObject of class "numeric": a (sorted)
vector containing the support of the discrete density function
.withArithlogical: used internally to issue warnings as to interpretation of arithmetics
.withSimlogical: used internally to issue warnings as to accuracy
.logExactlogical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExactlogical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetryobject of class "DistributionSymmetry";
used internally to avoid unnecessary calculations.
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 method
signature(object = "Pois"):
returns the slot lambda of the parameter of the distribution
signature(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@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
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. ## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.) 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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