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dist_f
The F Distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_f(df1, df2, ncp = NULL)
Arguments
df1 |
degrees of freedom. |
df2 |
degrees of freedom. |
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
Examples
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)