distr (version 2.9.5)

Binom-class: Class "Binom"

Description

The binomial distribution with size \(= n\), by default \(=1\), and prob \(= p\), by default \(=0.5\), has density $$p(x) = {n \choose x} {p}^{x} {(1-p)}^{n-x}$$ for \(x = 0, \ldots, n\).

C.f.rbinom

Objects from the Class

Objects can be created by calls of the form Binom(prob, size). This object is a binomial 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 "BinomParameter": the parameter of this distribution (prob, size), declared at its instantiation

r

Object of class "function": generates random numbers (calls function rbinom)

d

Object of class "function": density function (calls function dbinom)

p

Object of class "function": cumulative function (calls function pbinom)

q

Object of class "function": inverse of the cumulative function (calls function qbinom). The quantile is defined as the smallest value x such that F(x) >= p, where F is the cumulative 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 = "Binom", e2 = "Binom"): For two binomial distributions with equal probabilities the exact convolution formula is implemented thereby improving the general numerical accuracy.

initialize

signature(.Object = "Binom"): initialize method

prob

signature(object = "Binom"): returns the slot prob of the parameter of the distribution

prob<-

signature(object = "Binom"): modifies the slot prob of the parameter of the distribution

size

signature(object = "Binom"): returns the slot size of the parameter of the distribution

size<-

signature(object = "Binom"): modifies the slot size of the parameter of the distribution

Author

Thomas Stabla ,
Florian Camphausen ,
Peter Ruckdeschel ,
Matthias Kohl

See Also

BinomParameter-class DiscreteDistribution-class Naturals-class rbinom

Examples

B <- Binom(prob=0.5,size=1) # B is a binomial distribution with prob=0.5 and size=1.
r(B)(1) # # one random number generated from this distribution, e.g. 1
d(B)(1) # Density of this distribution is  0.5 for x=1.
p(B)(0.4) # Probability that x<0.4 is 0.5.
q(B)(.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(.)(.)
size(B) # size of this distribution is 1.
size(B) <- 2 # size of this distribution is now 2.
C <- Binom(prob = 0.5, size = 1) # C is a binomial distribution with prob=0.5 and size=1.
D <- Binom(prob = 0.6, size = 1) # D is a binomial distribution with prob=0.6 and size=1.
E <- B + C # E is a binomial distribution with prob=0.5 and size=3.
F <- B + D # F is an object of class LatticeDistribution.
G <- B + as(D,"DiscreteDistribution") ## DiscreteDistribution