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.

Examples

Run this code

# 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)

# }

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