Three-parameter Exponentiated Weibull distribution with
scale \(s\), first shape \(a\) (shape1, the
Weibull shape), and second shape \(b\) (shape2, the
exponentiation power). The distribution is supported on \(x > 0\)
and contains the ordinary Weibull (\(b = 1\)) and Exponential
(\(a = 1, b = 1\)) as special cases. L-moments are computed by
tanh-sinh (double-exponential) quadrature, which is well-conditioned
across the full positive parameter range. Fitting uses L-BFGS-B
minimisation seeded from the ExpWeibull_InitValues lookup
table with scale-free L-ratio matching and analytic scale derivation.
The probability density function is: $$f(x) = \frac{b a}{s} \left(\frac{x}{s}\right)^{a-1} \exp\left(-\left(\frac{x}{s}\right)^a\right) \left(1 - \exp\left(-\left(\frac{x}{s}\right)^a\right)\right)^{b-1}, \quad x > 0$$ where:
\(s\) — scale parameter (
scale)\(a\) — first shape parameter (
shape1), the Weibull shape; a = 1 gives the exponential baseline\(b\) — second shape parameter (
shape2), the exponentiation power; b = 1 recovers the ordinary Weibull
Usage
pexpweibull(q, scale, shape1, shape2, log.p = FALSE)
dexpweibull(x, scale, shape1, shape2, log = FALSE)
qexpweibull(p, scale, shape1, shape2)
rexpweibull(n, scale, shape1, shape2)