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Statistical depth functions have been well studied for multivariate data and functional data but remained under-explored for point process until very recently Liu and Wu made their first attempt. Generally, neither depth functions for multivariate data nor for functional data are suitable for measuring the center-outward ranks of point process, since those traditional depth functions neglect the fact that point processes data are ordered and existing two types of randomness. To address this problem, we not only generalize a depth framework that includes 1) a probability term on cardinality of point process , 2) a conditional depth function given cardinality fixed and 3) a weight parameter (based on Liu and Wu's previous work), but also introduce two new conditional depth functions defined on inter-arrival times of point processes. Further, we propose five desirable properties for the conditional depth to robustly rank point process given cardinality fixed. The asymptotic behavior of our proposed depth framework are investigated. Through simulations we demonstrate that our proposed depth framework and conditional depth functions reveals the center-outward ranks of given point process realizations. And through classification performance on real neural spike trains, we illustrate that our framework have the flexibility to address various classification issues.