FDistributionNoncentral: Noncentral F Distribution Class

Description Details Value Distribution support Default Parameterisation Omitted Methods Also known as Super classes Public fields Active bindings Methods Author(s) References See Also

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)

Omitted Methods

N/A

Also known as

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(...)
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.

Usage
FDistributionNoncentral$variance(...)
Arguments
...

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.

Author(s)

Jordan Deenichin

References

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

See Also

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, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull, WeightedDiscrete


distr6 documentation built on Sept. 6, 2021, 9:10 a.m.