Total positivity of Markov chains and the failure rate character of some first passage times

被引：4

作者：

Lee, SJ ^{[1
]}

Lynch, J ^{[1
]}

机构：

[1] UNIV S CAROLINA, DEPT STAT, COLUMBIA, SC 29208 USA

来源：

ADVANCES IN APPLIED PROBABILITY | 1997年 / 29卷 / 03期

关键词：

failure rate; log-concavity; total positivity; multivariate total positivity;

D O I：

10.2307/1428083

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：

It is shown that totally positive order 2 (TP2) properties of the infinitesimal generator of a continuous-time Markov chain with totally ordered state space carry over to the chain's transition distribution function. For chains with such properties, failure rate characteristics of the first passage times are established. For Markov chains with partially ordered state space, it is shown that the first passage times have an IFR distribution under a multivariate total positivity condition on the transition function.

引用

页码：713 / 732

页数：20

共 14 条

[1]

BARLOW RE, 1975, STATISTICAL THEORY R

[2] ON THE 1ST PASSAGE TIME DISTRIBUTION FOR A CLASS OF MARKOV-CHAINS [J].