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
- Keywords
- distribution
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 instantiationr
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
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).
# }