3-parameter Weibull Distribution — Weibull3 • anyFit

Three-parameter Weibull distribution with location $\mu$, scale $\sigma$, and shape $k$. The distribution is lower-bounded at the location parameter and generalises the Exponential ($k = 1$) and Rayleigh ($k = 2$) distributions. Fitting is performed via closed-form L-moments. An optional fixed lower bound is supported.

The probability density function is: $$f(x) = \frac{k}{\sigma} \left(\frac{x - \mu}{\sigma}\right)^{k-1} \exp\left(-\left(\frac{x - \mu}{\sigma}\right)^k\right), \quad x \ge \mu$$ where:

$\mu$ — location parameter (location)
$\sigma$ — scale parameter (scale)
$k$ — shape parameter (shape)

Usage

dweibull(x, location, scale, shape)

pweibull(q, location, scale, shape)

qweibull(p, location, scale, shape)

rweibull(n, location, scale, shape)

Arguments

x, q: vector of quantiles.
location: location parameter.
scale: scale parameter.
shape: shape parameter.
p: vector of probabilities.
n: number of observations. If length(n) > 1, the length is taken as the number required.