Rockwell Automation Arena Basic Edition Users Guide - Manual (Page 70)

A RENA B ASIC E DITION U SER ’ S G UIDE
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DiscreteDISCRETE(CumP
1
, Val
1
, . . ., CumP
n
, Val
n
)
(c
1
, x
1
, . . ., c
n
, x
n
)
The DISCRETE function in Arena returns a sample from a user-defined discrete probabil-
ity distribution. The distribution is defined by the set of n possible discrete values
(denoted by x
1
, x
2
, . . . , x
n
) that can be returned by the function and the cumulative proba-
bilities (denoted by c
1
, c
2
, . . . , c
n
) associated with these discrete values. The cumulative
probability (c
j
) for x
j
is defined as the probability of obtaining a value that is less than or
equal to x
j
. Hence, c
j
is equal to the sum of p(x
k
) for k going from 1 to j. By definition,
c
n
= 1.
{x
1
, x
2
, . . ., x
n
}
The discrete empirical distribution is often used to incorporate discrete empirical data
directly into the model. This distribution is frequently used for discrete assignments such
as the job type, the visitation sequence, or the batch size for an arriving entity.
Probability
Mass
Function
Cumulative
Distribution
Function
Parameters
Range
Applications
p(x
j
) = c
j
– c
j-1
where c
0
= 0