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proportions of variables (Hines and Montgomery [15]). This estimator examines
whether an empirical distribution of a variable matches a known probability
distribution of that variable. Again, because we assumed that a huge amount of
data were involved in building the incremental model, it is reasonable to assume
that the true population distribution of any variable in the given incremental model
is accurately estimated by the previous
K
periods.
The objective is to decide whether to accept the following null hypothesis for
every variable
X
of interest:
H
0
: the variable
X
's population is stationary between periods.
H
1
: otherwise.
The decision is made by the following equation:
1
x
x
(
iK
iK
1
)
2
j
n
n
¦
X
2
n
K
K
1
(4.4)
.
p
K
x
i
1
iK
1
n
K
1
2
2
1
X
p
D
F
then the base assumption that the variable
X
's
distribution has been stationary in period
K
is not accepted (see also Montgomery
and Runger [30]).
In Eq. (4.4);
n
K
is the number of records in the
K
th period;
!
(
j
1
If
n
is the number
K
1
K
;
i
x
is the number of records belonging to the
i
th class of variable
X
in the
K
th period;
1
of records in periods 1, ... ,
x
is the number of records belonging
iK
1
K
1
to the
i
th class of variable
X
in periods 1,...,
.
4.2.4 Methodology
This section describes the algorithmic usage of the previous estimators.
Inputs:
G
is the algorithm used for the DM classification model.
M
is the model used for DM representation.
V
is the validation method in use.
K
is the number of periods.
is the desired confidence level for the procedure.
D
Outputs:
is the Change Detection estimator 1 - Pvalue.
CD (D)
XP (D)
is the Pearson's estimator 1 - Pvalue.
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