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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:
The equation of the proportion of the random variable which is higher than the value Z to its region A is:
Under the condition of threshold value Z, the random function is a binomial distribution, and its expectation is:
The equation of the expectations of and
The descriptions of the cross covariance, variance, and semi-variance of the 2 indicator functionsand
with distance h are presented respectively as follows:
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