二项序列作为更新序列的特征刻画  

CHARACTERIZATION FOR BINOMIAL SEQUENCES AMONG RENEWAL SEQUENCES

作　　者：成世学 

机构地区：[1]Information Department of People's University of China, Beijing 100872

出　　处：《高校应用数学学报（A辑）》1992年第1期 114-128,共15页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：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.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.

关 键 词：二项序列 更新序列 几何分布 

分 类 号：O211[理学—概率论与数理统计;理学—数学]