Weibull: Create a Weibull distribution

Description Usage Arguments Details Value See Also Examples

View source: R/Weibull.R

Description

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

Usage

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Weibull(shape, scale)

Arguments

shape

The shape parameter k. Can be any positive real number.

scale

The scale parameter λ. Can be any positive real number.

Details

We recommend reading this documentation on https://alexpghayes.github.io/distributions3/, where the math will render with additional detail and much greater clarity.

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

Value

A Weibull object.

See Also

Other continuous distributions: Beta(), Cauchy(), ChiSquare(), Erlang(), Exponential(), FisherF(), Frechet(), GEV(), GP(), Gamma(), Gumbel(), LogNormal(), Logistic(), Normal(), RevWeibull(), StudentsT(), Tukey(), Uniform()

Examples

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set.seed(27)

X <- Weibull(0.3, 2)
X

random(X, 10)

pdf(X, 2)
log_pdf(X, 2)

cdf(X, 4)
quantile(X, 0.7)

distributions3 documentation built on Jan. 4, 2022, 1:07 a.m.