Pois-class

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

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.

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 \(F(x) \ge p\), 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

See Also

PoisParameter-class DiscreteDistribution-class Naturals-class rpois

Aliases

• Pois-class
• Pois
• initialize,Pois-method

Examples

# NOT RUN {
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).
# }