THE DISTRIBUTIONS OF CERTAIN RECORD STATISTICS FROM A RANDOM NUMBER OF OBSERVATIONS

被引：9

作者：

BUNGE, JA ^{[1
]}

NAGARAJA, HN ^{[1
]}

机构：

[1] OHIO STATE UNIV,DEPT STAT,COLUMBUS,OH 43210

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1991年 / 38卷 / 01期

关键词：

RANDOM RECORD MODEL; RECORD VALUES; NUMBER OF RECORDS; INTERRECORD COUNTS; POINT PROCESSES; PARTIAL FRACTION EXPANSION; GEOMETRIC DISTRIBUTION; NEGATIVE BINOMIAL DISTRIBUTION;

D O I：

10.1016/0304-4149(91)90077-P

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Suppose we observe a random number N of independent identically distributed random variables in sequence. The record values are the successive maxima of this sequence. Assuming that N and the observations are independent, we obtain the joint distribution of the number of records and their values. Using this, the dependence structures of record values and interrecord counts are studied; this yields a necessary and sufficient condition for N to have geometric tail. In addition, we obtain the distribution of the number of records. When N is negative binomial, the expressions can be simplified; in one case the number of records has an exact Poisson distribution. Our results are applied to point process models considered by Gaver (1976) and Westcott (1977). Our results remain applicable when the assumption of identical distribution is relaxed to allow the distribution to change after a record event, as proposed by Pfeifer (1982).

引用

页码：167 / 183

页数：17

共 13 条

[1] INVARIANT RECORD PROCESSES AND APPLICATIONS TO BEST CHOICE MODELING [J].