Weibull random variable
X is a Weibull random variable if it has a probability density function, given by
fX(x)=γα(x-μα)γ-1e-(x-μα)γ |
where α,γ,μ∈ℝ, α,γ>0 and x≥μ. α is the scale parameter, γ is the shape parameter, and μ is the location parameter.
Notation for X having a Weibull distribution is X∼Wei(α,γ,μ). Usually, the location and scale parameters are dropped by the transformation
Y=X-μα |
so that Y∼Wei(γ):=. The resulting distribution is called the standard Weibull, or Rayleigh distribution:
: Given a standard Weibull distribution :
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, where is the gamma function
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Median =
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Mode
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iff , the exponential distribution
with parameter
Remark. The Weibull distribution is often used to model reliability or lifetime of such as light bulbs.
Title | Weibull random variable |
---|---|
Canonical name | WeibullRandomVariable |
Date of creation | 2013-03-22 14:26:44 |
Last modified on | 2013-03-22 14:26:44 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 8 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 62N99 |
Classification | msc 62E15 |
Classification | msc 60E05 |
Classification | msc 62P05 |
Synonym | Weibull distribution |
Synonym | Rayleigh distribution |