FDistribution: '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..

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

FDistribution$new(df1 = 1, df2 = 1, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`df1, df2`	numeric	degrees of freedom.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The 'F' distribution is parameterised with df1 and df2 as positive numerics.

Public Variables

Variable	Return
`name`	Name of distribution.
`short_name`	Id of distribution.
`description`	Brief description of distribution.

Public Methods

Accessor Methods	Link
`decorators()`	`decorators`
`traits()`	`traits`
`valueSupport()`	`valueSupport`
`variateForm()`	`variateForm`
`type()`	`type`
`properties()`	`properties`
`support()`	`support`
`symmetry()`	`symmetry`
`sup()`	`sup`
`inf()`	`inf`
`dmax()`	`dmax`
`dmin()`	`dmin`
`skewnessType()`	`skewnessType`
`kurtosisType()`	`kurtosisType`



Statistical Methods	Link
`pdf(x1, ..., log = FALSE, simplify = TRUE)`	`pdf`
`cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)`	`cdf`
`quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)`	`quantile.Distribution`
`rand(n, simplify = TRUE)`	`rand`
`mean()`	`mean.Distribution`
`variance()`	`variance`
`stdev()`	`stdev`
`prec()`	`prec`
`cor()`	`cor`
`skewness()`	`skewness`
`kurtosis(excess = TRUE)`	`kurtosis`
`entropy(base = 2)`	`entropy`
`mgf(t)`	`mgf`
`cf(t)`	`cf`
`pgf(z)`	`pgf`
`median()`	`median.Distribution`
`iqr()`	`iqr`



Parameter Methods	Link
`parameters(id)`	`parameters`
`getParameterValue(id, error = "warn")`	`getParameterValue`
`setParameterValue(..., lst = NULL, error = "warn")`	`setParameterValue`



Validation Methods	Link
`liesInSupport(x, all = TRUE, bound = FALSE)`	`liesInSupport`
`liesInType(x, all = TRUE, bound = FALSE)`	`liesInType`



Representation Methods	Link
`strprint(n = 2)`	`strprint`
`print(n = 2)`	`print`
`summary(full = T)`	`summary.Distribution`
`plot()`	Coming Soon.
`qqplot()`	Coming Soon.

Details

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 $μ, ν > 0$ .

The distribution is supported on the Positive Reals.

cf is omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

References

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

Examples

Run this code

# NOT RUN {
x <- FDistribution$new(df1 = 1, df2 = 3)

# Update parameters
x$setParameterValue(df2 = 10)
x$parameters()

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }

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