
A • STATISTICAL DISTRIBUTIONS
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• • • • •
A • Statistical Distributions
Weibull(
β
,
α
)WEIBULL(Beta, Alpha) or WEIB(Beta, Alpha)
Shape parameter (
α
) and scale parameter (
β
) specified as positive real values.
[0, + )
, where Γ is the complete gamma function (see gamma distribution).
Probability
Density
Function
f(x)
0
x
a=1/2
a=1
a=2
a=3
f(x) =
0otherwise
for x > 0
aβ
a–
x
a 1–
e
x β⁄()
a
–
Parameters
Range
∞
Mean
β
a
---
Γ
1
a
---
⎝⎠
⎛⎞
Variance
β
2
a
-----
2Γ
2
a
---
⎝⎠
⎛⎞
1
a
---
Γ
1
a
---
⎝⎠
⎛⎞
2
⎭
⎬
⎫
–
⎩
⎨
⎧
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