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.

## Value

Returns an R6 object inheriting from class SDistribution.

## Details

The Noncentral F distribution parameterised with two degrees of freedom parameters, $$\mu, \nu$$, and location, $$\lambda$$, # nolint is defined by the pdf, $$f(x) = \sum_{r=0}^{\infty} ((exp(-\lambda/2)(\lambda/2)^r)/(B(\nu/2, \mu/2+r)r!))(\mu/\nu)^{\mu/2+r}(\nu/(\nu+x\mu))^{(\mu+\nu)/2+r}x^{\mu/2-1+r}$$ for $$\mu, \nu > 0, \lambda \ge 0$$.

## Distribution support

The distribution is supported on the Positive Reals.

## Default Parameterisation

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

N/A

N/A

## 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, Arrdist, 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

Jordan Deenichin

## 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.

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

Inherited methods

### Method new()

Creates a new instance of this R6 class.

#### Arguments

...

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.

#### Arguments

deep

Whether to make a deep clone.