THE JOINT DISTRIBUTION OF THE NUMBER OF OCCURRENCES OF 2 INTERRELATEDPOISSON PROCESSES

The focus of this paper is the distribution for the number of occurren ces of two independent but interrelated Poisson processes, to be named the joint imputed Poisson distribution. From its inception, the resea rch was motivated by a problem facing the electric power industry. Pow er surges, which are observable, represent occurrences of the imputing process. Circuit breaker breakdowns, which cannot be seen taking plac e, constitute occurrences of the imputed process. Though not observabl e, at each occurrence of the imputing process, knowledge about the imp uted process is obtained. Occurrences of the imputed process are revea led only as the result of periodic inspection, or with far greater cos t at the subsequent occurrence of the imputing process. A comprehensiv e treatment of the joint imputed Poisson distribution for the number o f occurrences of the two processes over a fixed time period was presen ted by Cuffe. Because these probabilistic results had to be derived fr om first principles, a lengthy, rigorous mathematical exposition is no t appropriate in this forum. Rather, we concentrate here on a presenta tion of results with only highlights of their proofs.