View source: R/ReversedWeibull.R
RevWeibull | R Documentation |
The reversed (or negated) Weibull distribution is a special case of the
\link{GEV}
distribution, obtained when the GEV shape parameter ξ
is negative. It may be referred to as a type III extreme value
distribution.
RevWeibull(location = 0, scale = 1, shape = 1)
location |
The location (maximum) parameter m.
|
scale |
The scale parameter s.
|
shape |
The scale parameter α.
|
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 reversed Weibull random variable with
location parameter location
= m, scale parameter scale
=
s, and shape parameter shape
= α.
An RevWeibull(m, s, α) distribution is equivalent to a
\link{GEV}
(m - s, s / α, -1 / α) distribution.
If X has an RevWeibull(m, λ, k) distribution then
m - X has a \link{Weibull}
(k, λ) distribution,
that is, a Weibull distribution with shape parameter k and scale
parameter λ.
Support: (-∞, m).
Mean: m + sΓ(1 + 1/α).
Median: m + s(\ln 2)^(1/α).
Variance: s^2 [Γ(1 + 2 / α) - Γ(1 + 1 / α)^2].
Probability density function (p.d.f):
f(x) = (α / s) [-(x - m) / s] ^ (α - 1) exp{-[-(x - m) / s] ^ α}
for x < m. The p.d.f. is 0 for x >= m.
Cumulative distribution function (c.d.f):
F(x) = exp{-[-(x - m) / s] ^ α}
for x < m. The c.d.f. is 1 for x >= m.
A RevWeibull
object.
Other continuous distributions:
Beta()
,
Cauchy()
,
ChiSquare()
,
Erlang()
,
Exponential()
,
FisherF()
,
Frechet()
,
GEV()
,
GP()
,
Gamma()
,
Gumbel()
,
LogNormal()
,
Logistic()
,
Normal()
,
StudentsT()
,
Tukey()
,
Uniform()
,
Weibull()
set.seed(27) X <- RevWeibull(1, 2) X random(X, 10) pdf(X, 0.7) log_pdf(X, 0.7) cdf(X, 0.7) quantile(X, 0.7) cdf(X, quantile(X, 0.7)) quantile(X, cdf(X, 0.7))
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.