Class "Binom"
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 can be created by calls of the form Binom(prob, size).
This object is a binomial 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 "BinomParameter": the parameter
of this distribution (prob, size), declared at its
instantiation
rObject of class "function": generates random
numbers (calls function rbinom)
dObject of class "function": density function (calls
function dbinom)
pObject of class "function": cumulative function
(calls function pbinom)
qObject 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.
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 = "Binom", e2 = "Binom"): For two binomial
distributions with equal probabilities the exact convolution
formula is implemented thereby improving the general numerical
accuracy.
signature(.Object = "Binom"): initialize method
signature(object = "Binom"): returns the slot prob
of the parameter of the distribution
signature(object = "Binom"): modifies the slot
prob of the parameter of the distribution
signature(object = "Binom"): returns the slot size
of the parameter of the distribution
signature(object = "Binom"): modifies the slot
size of the parameter of the distribution
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
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
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