On the Distribution of the Number of Success Runs in a Continuous Time Markov Chain

被引：4

作者：

Michael, Boutsikas V. ^{[1
]}

Eutichia, Vaggelatou ^{[2
]}

机构：

[1] Univ Piraeus, Dept Stat & Insurance Sci, Piraeus, Greece

[2] Natl & Kapodistrian Univ Athens, Dept Math, Athens, Greece

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2020年 / 22卷 / 03期

关键词：

Run statistics; Marked point process; Continuous-time Markov chain; Waiting time; Exact distribution; Markov chain imbedding technique; Generating function; Laplace transform; Secondary; STATISTICS; SEQUENCE;

D O I：

10.1007/s11009-019-09743-3

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：

We propose a continuous-time adaptation of the well-known concept of success runs by considering a marked point process with two types of marks (success-failure) that appear according to an appropriate continuous-time Markov chain. By constructing a bivariate imbedded process (consisting of a run-counting and a phase process), we offer recursive formulas and generating functions for the distribution of the number of runs and the waiting time until the appearance of then-th success run. We investigate the three most popular counting schemes: (i) overlapping runs of lengthk, (ii) non-overlapping runs of lengthkand (iii) runs of length at leastk. We also present examples of applications regarding: the total penalty cost in a maintenance reliability system, the number of risky situations in a non-life insurance portfolio and the number of runs of increasing (or decreasing) asset price movements in high-frequency financial data.

引用

页码：969 / 993

页数：25

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