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Generalized moments of the distance between Poisson process events

Author

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  • Adolfo M. D. da Silva
  • C. E. G. Otiniano

Abstract

By using Fox’s H function, we derive the a-th absolute moment from the difference between arrival times X1,X2,… and Y1,Y2,… from two independent Poisson processes with rates λ1>0 and λ2>0. In addition, we present numerical results and graphical illustrations of our results. A possible application of a-th absolute moment is in a network of two sensors that are placed randomly according to two Poisson processes with rates not necessarily equal. If each sensor has a different detection function, the hypothesis that the rates of the processes are different is natural. The sum of the a-th absolute moment is the expected transportation cost between events X1,X2,…Xn and Y1,Y2,…Yn.

Suggested Citation

  • Adolfo M. D. da Silva & C. E. G. Otiniano, 2022. "Generalized moments of the distance between Poisson process events," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(8), pages 2330-2342, April.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:8:p:2330-2342
    DOI: 10.1080/03610926.2021.1968901
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