Weibull(b, a), Βa --- γ 1 a, A γ 2 a --- ⎝ ⎠ ⎛ ⎞ 1 a --- γ 1 a – Rockwell Automation Arena Basic Edition Users Guide User Manual
Page 81
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A
•
S
TATISTICAL
D
ISTRIBUTIONS
75
•
•
•
• •
A •
Statis
tical
Dis
tribu
tions
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) =
0
otherwise
for x
> 0
a
β
a
–
x
a 1
–
e
x
β
⁄
(
)
a
–
Parameters
Range
∞
Mean
β
a
---
Γ 1
a
---
⎝ ⎠
⎛ ⎞
Variance
β
2
a
----- 2
Γ 2
a
---
⎝ ⎠
⎛ ⎞ 1
a
---
Γ 1
a
---
⎝ ⎠
⎛ ⎞
2
⎭
⎬
⎫
–
⎩
⎨
⎧
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