RevWeibull {distributions3}R Documentation

Create a reversed Weibull distribution


The reversed (or negated) Weibull distribution is a special case of the ⁠\link{GEV}⁠ distribution, obtained when the GEV shape parameter \xi is negative. It may be referred to as a type III extreme value distribution.


RevWeibull(location = 0, scale = 1, shape = 1)



The location (maximum) parameter m. location can be any real number. Defaults to 0.


The scale parameter s. scale can be any positive number. Defaults to 1.


The scale parameter \alpha. shape can be any positive number. Defaults to 1.


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In the following, let X be a reversed Weibull random variable with location parameter location = m, scale parameter scale = s, and shape parameter shape = \alpha. An RevWeibull(m, s, \alpha) distribution is equivalent to a ⁠\link{GEV}⁠(m - s, s / \alpha, -1 / \alpha) distribution.

If X has an RevWeibull(m, \lambda, k) distribution then m - X has a ⁠\link{Weibull}⁠(k, \lambda) distribution, that is, a Weibull distribution with shape parameter k and scale parameter \lambda.

Support: (-\infty, m).

Mean: m + s\Gamma(1 + 1/\alpha).

Median: m + s(\ln 2)^{1/\alpha}.

Variance: s^2 [\Gamma(1 + 2 / \alpha) - \Gamma(1 + 1 / \alpha)^2].

Probability density function (p.d.f):

f(x) = \alpha s ^ {-1} [-(x - m) / s] ^ {\alpha - 1}% \exp\{-[-(x - m) / s] ^ {\alpha} \}

for x < m. The p.d.f. is 0 for x \geq m.

Cumulative distribution function (c.d.f):

F(x) = \exp\{-[-(x - m) / s] ^ {\alpha} \}

for x < m. The c.d.f. is 1 for x \geq m.


A RevWeibull object.

See Also

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



X <- RevWeibull(1, 2)

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))

[Package distributions3 version 0.2.1 Index]