'F' Distribution Class
Mathematical and statistical functions for the 'F' distribution, which is commonly used in ANOVA testing and is the ratio of scaled Chi-Squared distributions..
The 'F' distribution parameterised with two degrees of freedom parameters, μ, ν, is defined by the pdf,
f(x) = Γ((μ + ν)/2) / (Γ(μ/2) Γ(ν/2)) (μ/ν)^{μ/2} x^{μ/2 - 1} (1 + (μ/ν) x)^{-(μ + ν)/2}
for μ, ν > 0.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on the Positive Reals.
F(df1 = 1, df2 = 1)
N/A
N/A
distr6::Distribution -> distr6::SDistribution -> FDistribution
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.
new()
Creates a new instance of this R6 class.
FDistribution$new(df1 = NULL, df2 = NULL, decorators = NULL)
df1(numeric(1))
First degree of freedom of the distribution defined on the positive Reals.
df2(numeric(1))
Second degree of freedom of the distribution defined on the positive Reals.
decorators(character())
Decorators to add to the distribution during construction.
mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
FDistribution$mean(...)
...Unused.
mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
FDistribution$mode(which = "all")
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.
FDistribution$variance(...)
...Unused.
skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution.
FDistribution$skewness(...)
...Unused.
kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment,
k_X = E_X[((x - μ)/σ)^4]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.
FDistribution$kurtosis(excess = TRUE, ...)
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
entropy()
The entropy of a (discrete) distribution is defined by
- ∑ (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for continuous distributions.
FDistribution$entropy(base = 2, ...)
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)
...Unused.
mgf()
The moment generating function is defined by
mgf_X(t) = E_X[exp(xt)]
where X is the distribution and E_X is the expectation of the distribution X.
FDistribution$mgf(t, ...)
t(integer(1))
t integer to evaluate function at.
...Unused.
pgf()
The probability generating function is defined by
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
FDistribution$pgf(z, ...)
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
setParameterValue()
Sets the value(s) of the given parameter(s).
FDistribution$setParameterValue( ..., lst = NULL, error = "warn", resolveConflicts = FALSE )
...ANY
Named arguments of parameters to set values for. See examples.
lst(list(1))
Alternative argument for passing parameters. List names should be parameter names and list values
are the new values to set.
error(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".
resolveConflicts(logical(1))
If FALSE (default) throws error if conflicting parameterisations are provided, otherwise
automatically resolves them by removing all conflicting parameters.
clone()
The objects of this class are cloneable with this method.
FDistribution$clone(deep = FALSE)
deepWhether to make a deep clone.
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,
FDistributionNoncentral,
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,
FDistributionNoncentral,
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
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