What is it about?
We consider two identical and independent Poisson processes. The expected absolute difference of the arrival times to the power a between two identical and independent Poisson processes we represent as the combination of the Pochhammer polynomials.
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Why is it important?
It is new nice closed formula for mathematical statistics for important expected absolute difference to the power between two Poisson processes. In the article it is presented methodology how to obtain similar formula for expected absolute difference to the power between two another random variables. New formulas are always useful.
Perspectives
1. From this results it is easy to obtain nice closed formula for generalization -power Gini index for Gamma distribution. The presented methodology allow to obtain power or weighted Gini index as well another generalization for another class of distribution. Since Gini index is very well recognized in economy I believe that the new theoretical results are of interest. 2.Another application is in computer science. This paper is about probabilistic matching. It is still not well recognized part of computer science. I see potential application in practical sensor network, electrical engineering as well as theoretical part analysis of algorithms, randezvous problems, patrolling, etc.
Rafal Kapelko
Politechnika Wroclawska
Read the Original
This page is a summary of: On the moment distance of Poisson processes, Communication in Statistics- Theory and Methods, December 2017, Taylor & Francis,
DOI: 10.1080/03610926.2017.1406114.
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