FDistribution: 'F' Distribution Class
In RaphaelS1/distr6: The Complete R6 Probability Distributions Interface
FDistribution R Documentation
'F' Distribution Class
Description
Mathematical and statistical functions for the 'F' distribution, which
is commonly used in ANOVA testing and is the ratio of scaled Chi-Squared distributions..
Details
The 'F' distribution parameterised with two degrees of freedom parameters, \mu, \nu, is defined by the pdf,
f(x) = \Gamma((\mu + \nu)/2) / (\Gamma(\mu/2) \Gamma(\nu/2)) (\mu/\nu)^{\mu/2} x^{\mu/2 - 1} (1 + (\mu/\nu) x)^{-(\mu + \nu)/2}
for \mu, \nu > 0.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the Positive Reals.
Default Parameterisation
F(df1 = 1, df2 = 1)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> FDistribution
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
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Inherited methods
distr6::Distribution$cdf()distr6::Distribution$confidence()distr6::Distribution$correlation()distr6::Distribution$getParameterValue()distr6::Distribution$iqr()distr6::Distribution$liesInSupport()distr6::Distribution$liesInType()distr6::Distribution$median()distr6::Distribution$parameters()distr6::Distribution$pdf()distr6::Distribution$prec()distr6::Distribution$print()distr6::Distribution$quantile()distr6::Distribution$rand()distr6::Distribution$setParameterValue()distr6::Distribution$stdev()distr6::Distribution$strprint()distr6::Distribution$summary()distr6::Distribution$workingSupport()
Method new()
Creates a new instance of this R6 class.
Usage
FDistribution$new(df1 = NULL, df2 = 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.
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) = \sum p_X(x)*x
with an integration analogue for continuous distributions.
Usage
FDistribution$mean(...)
Arguments
...Unused.
Method mode()
The mode of a probability distribution is the point at which the pdf is
a local maximum, a distribution can be unimodal (one maximum) or multimodal (several
maxima).
Usage
FDistribution$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
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
FDistribution$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[\frac{x - \mu}{\sigma}^3]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
Usage
FDistribution$skewness(...)
Arguments
...Unused.
Method kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment,
k_X = E_X[\frac{x - \mu}{\sigma}^4]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
Excess Kurtosis is Kurtosis - 3.
Usage
FDistribution$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- \sum (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for
continuous distributions.
Usage
FDistribution$entropy(base = 2, ...)
Arguments
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)
...Unused.
Method 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.
Usage
FDistribution$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method pgf()
The probability generating function is defined by
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
FDistribution$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
FDistribution$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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,
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,
Arrdist,
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,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
RaphaelS1/distr6 documentation built on Feb. 24, 2024, 9:14 p.m.
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| FDistribution | R Documentation |
'F' Distribution Class
Description
Mathematical and statistical functions for the 'F' distribution, which is commonly used in ANOVA testing and is the ratio of scaled Chi-Squared distributions..
Details
The 'F' distribution parameterised with two degrees of freedom parameters, \mu, \nu, is defined by the pdf,
f(x) = \Gamma((\mu + \nu)/2) / (\Gamma(\mu/2) \Gamma(\nu/2)) (\mu/\nu)^{\mu/2} x^{\mu/2 - 1} (1 + (\mu/\nu) x)^{-(\mu + \nu)/2}
for \mu, \nu > 0.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the Positive Reals.
Default Parameterisation
F(df1 = 1, df2 = 1)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> FDistribution
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
Inherited methods
distr6::Distribution$cdf()distr6::Distribution$confidence()distr6::Distribution$correlation()distr6::Distribution$getParameterValue()distr6::Distribution$iqr()distr6::Distribution$liesInSupport()distr6::Distribution$liesInType()distr6::Distribution$median()distr6::Distribution$parameters()distr6::Distribution$pdf()distr6::Distribution$prec()distr6::Distribution$print()distr6::Distribution$quantile()distr6::Distribution$rand()distr6::Distribution$setParameterValue()distr6::Distribution$stdev()distr6::Distribution$strprint()distr6::Distribution$summary()distr6::Distribution$workingSupport()
Method new()
Creates a new instance of this R6 class.
Usage
FDistribution$new(df1 = NULL, df2 = NULL, decorators = NULL)
Arguments
df1(numeric(1))
First degree of freedom of the distribution defined on the positive Reals.df2(numeric(1))
Second degree of freedom of the distribution defined on the positive Reals.decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = \sum p_X(x)*x
with an integration analogue for continuous distributions.
Usage
FDistribution$mean(...)
Arguments
...Unused.
Method 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).
Usage
FDistribution$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise"all"returns all modes, otherwise specifies which mode to return.
Method variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the
covariance matrix is returned.
Usage
FDistribution$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[\frac{x - \mu}{\sigma}^3]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
Usage
FDistribution$skewness(...)
Arguments
...Unused.
Method kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment,
k_X = E_X[\frac{x - \mu}{\sigma}^4]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
Excess Kurtosis is Kurtosis - 3.
Usage
FDistribution$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
IfTRUE(default) excess kurtosis returned....Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- \sum (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for
continuous distributions.
Usage
FDistribution$entropy(base = 2, ...)
Arguments
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)...Unused.
Method mgf()
The moment generating function is defined by
mgf_X(t) = E_X[exp(xt)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
FDistribution$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method 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.
Usage
FDistribution$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at....Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
FDistribution$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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,
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,
Arrdist,
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,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
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