# Class "Binom" The binomial distribution with `size` $= n$, by default $=1$, and `prob` $= p$, by default $=0.5$, has density [REMOVE_ME]$$ p(x) = {n \choose x} {p}^{x} {(1-p)}^{n-x}p(x) = choose(n,x) p^x (1-p)^(n-x) [REMOVE_ME_2]$$ for $x = 0, \ldots, n$. C.f.`rbinom` class ## Description The binomial distribution with `size` $= n$, by default $=1$, and `prob` $= p$, by default $=0.5$, has density $$ p(x) = {n \choose x} {p}^{x} {(1-p)}^{n-x}p(x) = choose(n,x) p^x (1-p)^(n-x) $$ 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(s) Thomas Stabla statho3@web.de , Florian Camphausen fcampi@gmx.de , Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de , Matthias Kohl Matthias.Kohl@stamats.de ## See Also `BinomParameter-class` `DiscreteDistribution-class` `Naturals-class` `rbinom` ## Examples ```r 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 ```

Binom-class function