Rockwell Automation Arena Users Guide - Manual (Page 122)

A RENA U SER ’ S G UIDE
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ContinuousCONTINUOUS(CumP
1
, Val
1
, . . ., CumP
n
, Val
n
)
(c
1
, x
1
,. . ., c
n
,x
n
)
The CONTINUOUS function in Arena returns a sample from a user-defined distribution.
Pairs of cumulative probabilities c
j
(= CumP
j
) and associated values x
j
(= Val
j
) are speci-
fied. The sample returned will be a real number between x
1
and x
n
, and will be less than or
equal to each x
j
with corresponding cumulative probability c
j
. The x
j
’s must increase with
j. The c
j
’s must all be between 0 and 1, must increase with j, and c
n
must be 1.
The cumulative distribution function F(x) is piecewise linear with “corners” defined by
F(x
j
) = c
j
for j = 1, 2, . . ., n. Thus, for j > 2, the returned value will be in the interval (x
j–1
, x
j
]
Probability
Density
Function
Cumulative
Distribution
Function
f(x) =
c
1
if x = x
1
(a mass of probability c
1
at x
1
)
c
j
– c
j-1
if x
j-1
≤ x < x
j
, for j = 2, 3, . . ., n
0 if x < x
1
or x ≥ x
n
Parameters