# FDistributionNoncentral: Noncentral F Distribution Class In distr6: The Complete R6 Probability Distributions Interface

 FDistributionNoncentral R Documentation

## Noncentral F Distribution Class

### Description

Mathematical and statistical functions for the Noncentral F distribution, which is commonly used in ANOVA testing and is the ratio of scaled Chi-Squared distributions.

### Details

The Noncentral F distribution parameterised with two degrees of freedom parameters, μ, ν, and location, λ, # nolint is defined by the pdf,

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

for μ, ν > 0, λ ≥ 0.

### Value

Returns an R6 object inheriting from class SDistribution.

### Distribution support

The distribution is supported on the Positive Reals.

### Default Parameterisation

FNC(df1 = 1, df2 = 1, location = 0)

N/A

N/A

### Super classes

`distr6::Distribution` -> `distr6::SDistribution` -> `FDistributionNoncentral`

### 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
```FDistributionNoncentral\$new(
df1 = NULL,
df2 = NULL,
location = NULL,
decorators = NULL
)```
##### Arguments
`df1`

`(numeric(1))`
First degree of freedom of the distribution defined on the positive Reals.

`df2`

`(numeric(1))`
Second degree of freedom of the distribution defined on the positive Reals.

`location`

`(numeric(1))`
Location parameter, defined on the Reals.

`decorators`

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

#### Method `mean()`

The arithmetic mean of a (discrete) probability distribution X is the expectation

E_X(X) = ∑ p_X(x)*x

with an integration analogue for continuous distributions.

##### Usage
`FDistributionNoncentral\$mean(...)`
`...`

Unused.

#### Method `variance()`

The variance of a distribution is defined by the formula

var_X = E[X^2] - E[X]^2

where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

##### Usage
`FDistributionNoncentral\$variance(...)`
`...`

Unused.

#### Method `clone()`

The objects of this class are cloneable with this method.

##### Usage
`FDistributionNoncentral\$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`, `BetaNoncentral`, `Beta`, `Cauchy`, `ChiSquaredNoncentral`, `ChiSquared`, `Dirichlet`, `Erlang`, `Exponential`, `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`, `BetaNoncentral`, `Beta`, `Binomial`, `Categorical`, `Cauchy`, `ChiSquaredNoncentral`, `ChiSquared`, `Degenerate`, `DiscreteUniform`, `Empirical`, `Erlang`, `Exponential`, `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`