Generalized moments of the distance between Poisson process events
Adolfo Manoel Dias da Silva, Cira E. G. Otiniano · Communication in Statistics- Theory and Methods · 2021
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.