distr6 (version 1.3.6)

Binomial: Binomial Distribution Class

Description

Mathematical and statistical functions for the Binomial distribution, which is commonly used to model the number of successes out of a number of independent trials.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Binomial$new(size = 10, prob = 0.5, qprob = NULL, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
size	numeric	number of trials.
prob	numeric	probability of success.
qprob	numeric	probability of failure.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Binomial distribution is parameterised with size as a whole number, and either prob or qprob as a number between 0 and 1. These are related via, $$qprob = 1 - prob$$ If qprob is given then prob is ignored.

Public Variables

Variable	Return
name	Name of distribution.
short_name	Id of distribution.
description	Brief description of distribution.

Public Methods

Accessor Methods	Link
decorators	decorators
traits	traits
valueSupport	valueSupport
variateForm	variateForm
type	type
properties	properties
support	support
symmetry	symmetry
sup	sup
inf	inf
dmax	dmax
dmin	dmin
skewnessType	skewnessType
kurtosisType	kurtosisType

Statistical Methods Link pdf(x1, ..., log = FALSE, simplify = TRUE) pdf cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) cdf quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) quantile.Distribution rand(n, simplify = TRUE) rand mean() mean.Distribution variance() variance stdev() stdev prec() prec cor() cor skewness() skewness kurtosis(excess = TRUE) kurtosis entropy(base = 2) entropy mgf(t) mgf cf(t) cf pgf(z) pgf median() median.Distribution iqr() iqr mode(which = "all") mode

Parameter Methods Link parameters(id) parameters getParameterValue(id, error = "warn") getParameterValue setParameterValue(..., lst = NULL, error = "warn") setParameterValue

Validation Methods Link liesInSupport(x, all = TRUE, bound = FALSE) liesInSupport liesInType(x, all = TRUE, bound = FALSE) liesInType

Representation Methods Link strprint(n = 2) strprint print(n = 2) print summary(full = T) summary.Distribution

Details

The Binomial distribution parameterised with number of trials, n, and probability of success, p, is defined by the pmf, $$f(x) = C(n, x)p^x(1-p)^{n-x}$$ for \(n = 0,1,2,\ldots\) and \(p \ \epsilon \ [0,1]\), where \(C(a,b)\) is the combination (or binomial coefficient) function.

The distribution is supported on \({0, 1,...,n}\).

References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

See Also

listDistributions for all available distributions.

Examples

# NOT RUN {
# Can be parameterised with probability of success or failure
Binomial$new(prob = 0.2)
Binomial$new(qprob = 0.3)

x = Binomial$new() # Default is with prob = 0.5 and size = 10

# Update parameters
# When any parameter is updated, all others are too!
x$setParameterValue(size = 4, qprob = 0.1)
x$parameters()

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }