Weibull {distributions3} R Documentation

## Create a Weibull distribution

### Description

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

### Usage

Weibull(shape, scale)


### Arguments

 shape The shape parameter k. Can be any positive real number. scale The scale parameter \lambda. 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: \lambda \Gamma(1+1/k), where \Gamma is the gamma function.

Variance: \lambda [ \Gamma (1 + \frac{2}{k} ) - (\Gamma(1+ \frac{1}{k}))^2 ]

Probability density function (p.d.f):

 f(x) = \frac{k}{\lambda}(\frac{x}{\lambda})^{k-1}e^{-(x/\lambda)^k}, x \ge 0 

Cumulative distribution function (c.d.f):

F(x) = 1 - e^{-(x/\lambda)^k}, x \ge 0

Moment generating function (m.g.f):

\sum_{n=0}^\infty \frac{t^n\lambda^n}{n!} \Gamma(1+n/k), k \ge 1

### Value

A Weibull object.

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

### Examples


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)


[Package distributions3 version 0.2.1 Index]