Noncentral Beta Distribution Class

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.

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.

Distribution support

The distribution is supported on \([0, 1]\).

Default Parameterisation

BetaNC(shape1 = 1, shape2 = 1, location = 0)

Omitted Methods

N/A

Also known as

N/A

References

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

See also

Other continuous distributions: Arcsine, Beta, Cauchy, ChiSquaredNoncentral, ChiSquared, Dirichlet, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Gompertz, Gumbel, InverseGamma, Laplace, Logistic, Loglogistic, Lognormal, MultivariateNormal, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull

Other univariate distributions: Arcsine, Arrdist, Bernoulli, Beta, Binomial, Categorical, Cauchy, ChiSquaredNoncentral, ChiSquared, Degenerate, DiscreteUniform, Empirical, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Geometric, Gompertz, Gumbel, Hypergeometric, InverseGamma, Laplace, Logarithmic, Logistic, Loglogistic, Lognormal, Matdist, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull, WeightedDiscrete

Author

Jordan Deenichin

Super classes

distr6::Distribution -> distr6::SDistribution -> BetaNoncentral

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

alias

Alias of the distribution.

packages

Packages required to be installed in order to construct the distribution.

Active bindings

properties

Returns distribution properties, including skewness type and symmetry.

Methods

Public methods

• BetaNoncentral$new()

• BetaNoncentral$clone()

Inherited methods

• distr6::Distribution$cdf()
• distr6::Distribution$confidence()
• distr6::Distribution$correlation()
• distr6::Distribution$getParameterValue()
• distr6::Distribution$iqr()
• distr6::Distribution$liesInSupport()
• distr6::Distribution$liesInType()
• distr6::Distribution$median()
• distr6::Distribution$parameters()
• distr6::Distribution$pdf()
• distr6::Distribution$prec()
• distr6::Distribution$print()
• distr6::Distribution$quantile()
• distr6::Distribution$rand()
• distr6::Distribution$setParameterValue()
• distr6::Distribution$stdev()
• distr6::Distribution$strprint()
• distr6::Distribution$summary()
• distr6::Distribution$workingSupport()

---

Method new()

Creates a new instance of this R6 class.

Usage

BetaNoncentral$new(
  shape1 = NULL,
  shape2 = NULL,
  location = NULL,
  decorators = NULL
)

Arguments

shape1

(numeric(1))
First shape parameter, shape1 > 0.

shape2

(numeric(1))
Second shape parameter, shape2 > 0.

location

(numeric(1))
Location parameter, defined on the non-negative Reals.

decorators

(character())
Decorators to add to the distribution during construction.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

BetaNoncentral$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.