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Indicator Function
Assuming that in the spatial extent D, we obtain a sample random variable
at the location x and select a threshold value Z. The indicator function on each sample point
defining Z is:

In any region
within the above region D, the equation of the proportion of the random variable
which is less than the value Z to its region A is:
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The equation of the proportion of the random variable
which is higher than the value Z to its region A is:
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Under the condition of threshold value Z, the random function
is a binomial distribution, and its expectation is:
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The equation of the expectations of
and ![]()


The descriptions of the cross covariance, variance, and semi-variance of the 2 indicator functions
and
with distance h are presented respectively as follows:

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