Create a Weibull distribution
Generalization of the gamma distribution. Often used in survival and time-to-event analyses.
Weibull(shape, scale)
shape |
The shape parameter k. Can be any positive real number. |
scale |
The scale parameter λ. Can be any positive real number. |
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
A Weibull object.
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)
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