# dist_f: The F Distribution In distributional: Vectorised Probability Distributions

\lifecycle

stable

## Usage

 1 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

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 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)