Bernoulli: Bernoulli Distribution Class

Description

Mathematical and statistical functions for the Bernoulli distribution, which is commonly used to model a two-outcome scenario.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Bernoulli$new(prob = 0.5, qprob = NULL, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`prob`	numeric	probability of success.
`qprob`	numeric	probability of failure.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Bernoulli distribution is parameterised with prob or qprob as a number between 0 and 1. These are related via, $q p r o b = 1 - p r o b$ 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 Bernoulli distribution parameterised with probability of success, $p$ , is defined by the pmf, $f (x) = p, i f x = 1$ $f (x) = 1 - p, i f x = 0$ for $p \in [0, 1]$ .

The distribution is supported on ${0, 1}$ .

References

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

Examples

Run this code

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

x = Bernoulli$new(verbose = TRUE) # Default is with prob = 0.5

# Update parameters
# When any parameter is updated, all others are too!
x$setParameterValue(qprob = 0.3)
x$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)

# }

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