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.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on the Positive Reals.
FNC(df1 = 1, df2 = 1, location = 0)
N/A
N/A
distr6::Distribution -> distr6::SDistribution -> FDistributionNoncentral
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages required to be installed in order to construct the distribution.
propertiesReturns distribution properties, including skewness type and symmetry.
new()Creates a new instance of this R6 class.
FDistributionNoncentral$new( df1 = NULL, df2 = NULL, location = NULL, decorators = NULL )
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.
mean()The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X) = \sum p_X(x)*x$$ with an integration analogue for continuous distributions.
FDistributionNoncentral$mean(...)
...Unused.
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.
FDistributionNoncentral$variance(...)
...Unused.
clone()The objects of this class are cloneable with this method.
FDistributionNoncentral$clone(deep = FALSE)
deepWhether to make a deep clone.
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 \(\mu, \nu > 0, \lambda \ge 0\).
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