# 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.