dist_f: The F Distribution

Description Usage Arguments Details See Also Examples

View source: R/dist_f.R

Description

\lifecycle

stable

Usage

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dist_f(df1, df2, ncp = NULL)

Arguments

df1

degrees of freedom. Inf is allowed.

df2

degrees of freedom. Inf is allowed.

ncp

non-centrality parameter. If omitted the central F is assumed.

Details

We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.

In the following, let X be a Gamma random variable with parameters shape = α and rate = β.

Support: x \in (0, ∞)

Mean: \frac{α}{β}

Variance: \frac{α}{β^2}

Probability density function (p.m.f):

f(x) = \frac{β^{α}}{Γ(α)} x^{α - 1} e^{-β x}

Cumulative distribution function (c.d.f):

f(x) = \frac{Γ(α, β x)}{Γ{α}}

Moment generating function (m.g.f):

E(e^(tX)) = \Big(\frac{β}{ β - t}\Big)^{α}, \thinspace t < β

See Also

stats::FDist

Examples

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dist <- dist_f(df1 = c(1,2,5,10,100), df2 = c(1,1,2,1,100))

dist
mean(dist)
variance(dist)
skewness(dist)
kurtosis(dist)

generate(dist, 10)

density(dist, 2)
density(dist, 2, log = TRUE)

cdf(dist, 4)

quantile(dist, 0.7)

distributional documentation built on Feb. 2, 2021, 5:09 p.m.