Arcsine: Arcsine Distribution Class

Description

Mathematical and statistical functions for the Arcsine distribution, which is commonly used in the study of random walks and as a special case of the Beta distribution.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Arcsine$new(lower = 0, upper = 1, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`lower`	integer	lower distribution limit.
`upper`	integer	upper distribution limit.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Arcsine distribution is parameterised with lower and upper as numerics.

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`



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 Arcsine distribution parameterised with lower, $a$, and upper, $b$, limits is defined by the pdf, $$f(x) = 1/(\pi\sqrt{(x-a)(b-x))}$$ for $-\infty < a \le b < \infty$.

The distribution is supported on $[a, b]$.

cf and mgf are omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

When the Standard Arcsine is constructed (default) then rbeta is used for sampling, otherwise via inverse transform

References

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

Examples

Run this code

# NOT RUN {
x = Arcsine$new(lower = 2, upper = 5)

# Update parameters
x$setParameterValue(upper = 4, lower = 1)
x$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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