distr6 (version 1.3.6)

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 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 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.

See Also

listDistributions for all available distributions. rbeta for the Beta distribution sampling function. CoreStatistics for numerical results.

Examples

# 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)

# }