DISTRIBUTION OF THE FINAL EXTENT OF A RUMOR PROCESS

被引：31

作者：

LEFEVRE, C ^{[1
]}

PICARD, P ^{[1
]}

机构：

[1] UNIV LYON 1,F-69622 VILLEURBANNE,FRANCE

来源：

JOURNAL OF APPLIED PROBABILITY | 1994年 / 31卷 / 01期

关键词：

MARTINGALES; GONTCHAROFF POLYNOMIALS;

D O I：

10.2307/3215250

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：

A rumour model due to Maki and Thompson (1973) is slightly modified to incorporate a continuous-time random contact process and varying individual behaviours in front of the rumour. Two important measures of the final extent of the rumour are provided by the ultimate number of people who have heard the rumour, and the total personal time units during which the rumour is spread. Our purpose in this note is to derive the exact joint distribution of these two statistics. That will be done by constructing a family of martingales for the rumour process and then using a particular family of Gontcharoff polynomials.

引用

页码：244 / 249

页数：6

共 8 条

[1]

[Anonymous], 1980, MATH MODELING EPIDEM

[2]

Daley DJ., 1965, IMA J APPL MATH, V1, P42, DOI [10.1093/imamat/1.1.42, DOI 10.1093/IMAMAT/1.1.42]

[3] A NONSTANDARD FAMILY OF POLYNOMIALS AND THE FINAL SIZE DISTRIBUTION OF REED-FROST EPIDEMIC PROCESSES [J].