Continuous probability distribution
Weibull (2-parameter)
Probability density function |
Cumulative distribution function |
Parameters |
scale shape |
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Support |
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PDF |
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CDF |
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Quantile |
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Mean |
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Median |
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Mode |
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Variance |
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Skewness |
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Excess kurtosis |
(see text) |
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Entropy |
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MGF |
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CF |
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Kullback–Leibler divergence |
see below |
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In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
The distribution is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1939,[1][2] although it was first identified by René Maurice Fréchet and first applied by Rosin & Rammler (1933) to describe a particle size distribution.
- ^ W. Weibull (1939). "The Statistical Theory of the Strength of Materials". Ingeniors Vetenskaps Academy Handlingar (151). Stockholm: Generalstabens Litografiska Anstalts Förlag: 1–45.
- ^ Bowers, et. al. (1997) Actuarial Mathematics, 2nd ed. Society of Actuaries.