dist_weibull {distributional}R Documentation

The Weibull distribution

Description

[Stable]

Generalization of the gamma distribution. Often used in survival and time-to-event analyses.

Usage

dist_weibull(shape, scale)

Arguments

shape, scale

shape and scale parameters, the latter defaulting to 1.

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 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

stats::Weibull

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)


[Package distributional version 0.3.2 Index]