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CHARACTERIZATION FOR BINOMIAL SEQUENCES AMONG RENEWAL SEQUENCES
作者姓名:成世学
作者单位:Information Department
基金项目:This work was supported by grant No.1880492 from the National Natural Science Foundation of China
摘    要:In this paper a binomial sequence is defined as a special sequence whose renewal lifes are identically distributed with a common geometric distribution. Therefore, it can be regarded as the discrete version of a Poisson process. Mainly, we discuss the characterization problem associated with binomial sequences. First, we sketch the properties of some important quantities of a renewal sequence. The emphasis of discussion is laid on the current life, the residual life and the total life. Then, we describe three main approaches to identify a geometric distribution. Finally, based on these concepts and techniques, we give a series of characterization theorems for a binomial sequence. These results are quite similar to those obtained for a Poisson process.


CHARACTERIZATION FOR BINOMIAL SEQUENCES AMONG RENEWAL SEQUENCES
Cheng Shixue.CHARACTERIZATION FOR BINOMIAL SEQUENCES AMONG RENEWAL SEQUENCES[J].Applied Mathematics A Journal of Chinese Universities,1992(1).
Authors:Cheng Shixue
Abstract:In this paper a binomial sequence is defined as a special sequence whose renewal lifes are identically distributed with a common geometric distribution. Therefore, it can be regarded as the discrete version of a Poisson process. Mainly, we discuss the characterization problem associated with binomial sequences. First, we sketch the properties of some important quantities of a renewal sequence. The emphasis of discussion is laid on the current life, the residual life and the total life. Then, we describe three main approaches to identify a geometric distribution. Finally, based on these concepts and techniques, we give a series of characterization theorems for a binomial sequence. These results are quite similar to those obtained for a Poisson process.
Keywords:Renewal Sequence  Sequence with Stationary and Independent Increments  Binomial Sequence  Renewal Life  Current life  Residual Life  Total Life  Geometric Distribution  
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