# BetaNoncentral: Noncentral Beta Distribution Class In distr6: The Complete R6 Probability Distributions Interface

 BetaNoncentral R Documentation

## Noncentral Beta Distribution Class

### 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.

### Value

Returns an R6 object inheriting from class SDistribution.

### Distribution support

The distribution is supported on [0, 1].

### Default Parameterisation

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

N/A

N/A

### 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.

`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

Inherited methods

#### 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.

Jordan Deenichin

### References

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

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`, `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`