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By using Fox’s  H  function, we derive the  a -th absolute moment from the difference between arrival timesandfrom two independent Poisson processes with ratesandIn 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 eventsand

Generalized moments of the distance between Poisson process events