symbolic dynamic models for highly varying power system loads

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where N=m+n. For large-sample populations, the above statistics can be approximated
based on the asymptotic distribution of J, suitably normalized, as min (m, n) tends to
infinity. Therefore,
J
*
= ( mn / N )
1/ 2
* max { F
i=
1,2... N
m
( Z(
i))
− G ( Z(
i))}
= d /( mnN)
n
1/ 2
* J .
For large samples,
∑ ∞ −
< → −
k 2 2
*
2k
s
0 J s)
{ ( 1)
e
k = −∞
P ( ,0} for{s>0, s ≤0.
The function Q(s) can be defined as
Q
∑ ∞ −
= − −
k 2 2
2k
s
( s)
1 ( 1) e , s>0
k = −∞
q * α is defined by
Q(q * α)=α
Table A.11 in [20] lists value of function Q(s), Thus α can also be obtained by the same
table. Appendix B shows a small illustrative example of the technique.
To test the earlier defined hypothesis, the KS method states,
Reject H 0 if J * ≥ q * α.
For example, from the cited table, for J * =1.5,
α=Q(1.5)=0.0222.
Which means the lowest significance level at which H 0 can be rejected is 2.22%. Thus for
the two populations to be identical, the desired value of α is 1.