Rockwell Automation Arena Users Guide - Manual (Page 127)

A • S TATISTICAL D ISTRIBUTIONS
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Stati
stica
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str
ibution
s
Gamma(
β
,
α
)GAMMA(Beta, Alpha) or GAMM(Beta, Alpha)
Shape parameter ( α ) and scale parameter ( β ) specified as positive real values.
[0, +
αβ
αβ 2
For integer shape parameters, the gamma is the same as the Erlang distribution. The
gamma is often used to represent the time required to complete some task (e.g., a
machining time or machine repair time).
Probability
Density
Function
f(x) =
0 otherwise
for x > 0
where Γ is the complete
gamma function given by
Γ α ( ) t
α 1 – e 1 – t d
0
∞ ∫
=
β α – x
α 1 – e x β ⁄ –
Γ α ( )
-----------------------------------
Parameters
Range
∞ )
Mean
Variance
Applications