We want to determine the grade of correlation between two sets of stationary time series, viz. a series of qualitative events A (t) and that of quantitative events B (t). For example, I) the passage of cold front A and the H-substance in the urine B or II) the spacial distribution of urine excretion B about the center of depression A. These two problems belong to the same category.
Let us consider a function δ(
t,
P), which means the appearance or non-appea ance of the event A at a point
P at a time
t and
δ(
t,
P)={1, for the appearance 0, for the non-appearance.
Let the observed value of B at a fixed point
Q at a time
t+s (
s=a parameter) be
v(
t+
s,
Q). Then in the first problem the function 1/
n ∑δ(
t,
Q)
v(
t+
s,
Q)=
m(
s,
Q), where the summation ∑ means the one by
t from
t=1 to
t=
N and
n=∑δ(
t,
Q), is a measure for the determination of the mode of correlation between A and B. This is the so-called n-method. In the second problem the function 1/
n ∑δ(
t,
P)
v(
t,
Q)=
m(
P,
Q) where
n=∑δ(
t,
P) may be utilised to determine the mode of spacial distribution. Because the surface
m=cont. is nothing but an inverted (about the point
Q!) figure of the spacial distribution in question (about the moving center A!).
To determine the mean error of the obtained result, we must at first transform the
m into the corresponding correlation coefficient
r, viz.
r(
s,
P)=∑δ(
t,
P)
v(
t+
s,
Q)/
n-∑
v(
t+
s,
Q)/
N/√
N/
n-1δ(
v)
where δ(
v) means the standard deviation of the
v(
t+
s,
Q) (
t=1, 2, …,
N), and secondly determine the mean error for
r. The direct application of 3 ∑-law for the
m might not be correct in these cases, because in these cases the
n has also a random character.
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