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Additive Property of Compound Generalized Poisson Process

Deng Chun

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Abstract

Generalized Poisson process often appears in the batch arrivals of customers or queuing problems of bulk service.In some literatures,probability generating function method is employed to prove the additive property of generalized-homogeneous Poisson process,based on which,this paper employs characteristic function method to prove that the compound generalized Poisson process has additive property similar to that of generalized-homogeneous Poisson process.

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What this paper is about

Generalized Poisson process often appears in the batch arrivals of customers or queuing problems of bulk service.In some literatures,probability generating function method is employed to prove the additive property of generalized-homogeneous Poisson process,based on which,this paper employs characteristic function method to prove that the compound generalized Poisson process has additive property similar to that of generalized-homogeneous Poisson process.

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Available abstract

Generalized Poisson process often appears in the batch arrivals of customers or queuing problems of bulk service.In some literatures,probability generating function method is employed to prove the additive property of generalized-homogeneous Poisson process,based on which,this paper employs characteristic function method to prove that the compound generalized Poisson process has additive property similar to that of generalized-homogeneous Poisson process.

Key concepts: Compound Poisson process, Poisson distribution, Property (philosophy), Compound Poisson distribution, Poisson process, Mathematics, Applied mathematics, Zero-inflated model

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