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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 functionsandwith distance h are presented respectively as follows:

 

 

 


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