Weibull Distribution
X ~ Weibull(k, λ)
Flexible-Hazard Lifetime Family • Published July 20, 2026
The reliability engineer's default lifetime model: history from Fréchet's extreme-value theory and Rosin-Rammler particle sizing through Waloddi Weibull's 1951 paper, a single shape parameter that spans decreasing, constant, and increasing hazard rates (the reliability 'bathtub curve'), a rare fully closed-form CDF and quantile function, a Fisher information matrix verified in closed form via the Euler-Mascheroni constant, and simulation via direct inverse-transform sampling.
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About This Reference Sheet
The reliability engineer's default lifetime model: history from Fréchet's extreme-value theory and Rosin-Rammler particle sizing through Waloddi Weibull's 1951 paper, a single shape parameter that spans decreasing, constant, and increasing hazard rates (the reliability 'bathtub curve'), a rare fully closed-form CDF and quantile function, a Fisher information matrix verified in closed form via the Euler-Mascheroni constant, and simulation via direct inverse-transform sampling.
Support
x ∈ (0, ∞)
Parameters
k > 0 (shape), λ > 0 (scale)