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