BetaNoncentral: Noncentral Beta Distribution Class

Description

Mathematical and statistical functions for the Noncentral Beta distribution, which is commonly used as the prior in Bayesian modelling.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

BetaNoncentral$new(shape1 = 1, shape2 = 1, location = 0, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`shape1, shape2`	numeric	positive shape parameter.
`location`	numeric	location (ncp in rstats).

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Noncentral Beta distribution is parameterised with shape1, shape2 as positive numerics, location as non-negative numeric.

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 Noncentral Beta distribution parameterised with two shape parameters, $\alpha, \beta$, and location, $\lambda$, is defined by the pdf, $$f(x) = exp(-\lambda/2) \sum_{r=0}^\infty ((\lambda/2)^r/r!) (x^{\alpha+r-1}(1-x)^{\beta-1})/B(\alpha+r, \beta)$$ for $\alpha, \beta > 0, \lambda \ge 0$, where $B$ is the Beta function.

The distribution is supported on $[0, 1]$.

mean, variance, skewness, kurtosis, entropy, mode, mgf and cf are omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

References

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

Examples

Run this code

# NOT RUN {
x = BetaNoncentral$new(shape1 = 2, shape2 = 5, location = 3)

# Update parameters
x$setParameterValue(shape1 = 1)
x$parameters()

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

summary(x)

# }

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