Definition:Weibull Distribution
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Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \R_{\ge 0}$.
$X$ is said to have a Weibull distribution if and only if it has probability density function:
- $\map {f_X} x = \alpha \beta^{-\alpha} x^{\alpha - 1} e^{-\paren {\frac x \beta}^\alpha}$
for $\alpha, \beta \in \R_{> 0}$.
Also see
- Results about the Weibull distribution can be found here.
Source of Name
This entry was named for Ernst Hjalmar Waloddi Weibull.
Sources
- Weisstein, Eric W. "Weibull Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WeibullDistribution.html