Rockwell Automation Arena Users Guide - Manual (Page 123)

A • S TATISTICAL D ISTRIBUTIONS
115
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A •
Stati
stica
l Di
str
ibution
s
with probability c
j
– c
j–1
; given that it is in this interval, it will be distributed uniformly over
it.
You must take care to specify c
1
and x
1
to get the effect you want at the left edge of the
distribution. The CONTINUOUS function will return (exactly) the value x
1
with
probability c
1
. Thus, if you specify c
1
> 0, this actually results in a mixed discrete-
continuous distribution returning (exactly) x
1
with probability c
1
, and with probability
1 – c
1
a continuous random variate on (x
1
, x
n
] as described above. The graph of F(x) above
depicts a situation where c
1
> 0. On the other hand, if you specify c
1
= 0, you will get a
(truly) continuous distribution on [x
1
, x
n
] as described above, with no “mass” of probability
at x
1
; in this case, the graph of F(x) would be continuous, with no jump at x
1
.
As an example use of the CONTINUOUS function, suppose you have collected a set of
data x
1
, x
2
, . . ., x
n
(assumed to be sorted into increasing order) on service times, for exam-
ple. Rather than using a fitted theoretical distribution from the Input Analyzer, you want
to generate service times in the simulation “directly” from the data, consistent with how
they’re spread out and bunched up, and between the minimum x
1
and the maximum x
n
you
observed. Assuming that you don’t want a “mass” of probability sitting directly on x
1
,
you’d specify c
1
= 0 and then c
j
= (j – 1)/(n – 1) for j = 2, 3, . . ., n.
[x
1
, x
n
]
The continuous empirical distribution is often used to incorporate actual data for continu-
ous random variables directly into the model. This distribution can be used as an alterna-
tive to a theoretical distribution that has been fitted to the data, such as in data that have a
multimodal profile or where there are significant outliers.
Range
Applications