Second-order statistics estimator functions in the spatial point process

Question

I'm running into a problem with edge corrector position perception. I would like to know when the edge corrector is placed in the numerator and when it is placed in the denominator, for example when estimating the K ou inhomogeneous K function and its extensions. Below are two estimators of the same function but with edge correctors in different positions.

Answer 1

There is no essential conflict between these equations. The edge correction factor is denoted by w_{y_i,y_j} in equation (1) and by e(x_i,x_j,r) in equation (2). In both cases the edge correction factor appears in the numerator.