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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 \(x \geq m\).