BetaNoncentral: Noncentral Beta Distribution Class

Description Details Value Constructor Constructor Arguments Constructor Details Public Variables Public Methods Author(s) References See Also Examples

Description

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

Details

The Noncentral Beta distribution parameterised with two shape parameters, α, β, and location, λ, is defined by the pdf,

f(x) = exp(-λ/2) ∑_{r=0}^∞ ((λ/2)^r/r!) (x^{α+r-1}(1-x)^{β-1})/B(α+r, β)

for α, β > 0, λ ≥ 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.

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.
verbose logical if TRUE parameterisation messages produced.

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.
package The package d/p/q/r are implemented in.

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

Author(s)

Jordan Deenichin

References

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

See Also

listDistributions for all available distributions. CoreStatistics for numerical results.

Examples

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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)

RaphaelS1/distr6 documentation built on March 30, 2020, 11:44 a.m.