dist_weibull
The Weibull distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_weibull(shape, scale)
Arguments
shape |
shape and scale parameters, the latter defaulting to 1. |
scale |
shape and scale parameters, the latter defaulting to 1. |
Details
Generalization of the gamma distribution. Often used in survival and time-to-event analyses.
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let X be a Weibull random variable with
success probability p = p.
Support: R^+ and zero.
Mean: λ Γ(1+1/k), where Γ is the gamma function.
Variance: λ [ Γ (1 + \frac{2}{k} ) - (Γ(1+ \frac{1}{k}))^2 ]
Probability density function (p.d.f):
f(x) = \frac{k}{λ}(\frac{x}{λ})^{k-1}e^{-(x/λ)^k}, x ≥ 0
Cumulative distribution function (c.d.f):
F(x) = 1 - e^{-(x/λ)^k}, x ≥ 0
Moment generating function (m.g.f):
∑_{n=0}^∞ \frac{t^nλ^n}{n!} Γ(1+n/k), k ≥ 1
See Also
Examples
dist <- dist_weibull(shape = c(0.5, 1, 1.5, 5), scale = rep(1, 4)) 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)