Compound Poisson Approximation for Multiple Runs in a Markov Chain |
| |
Authors: | Ourania Chryssaphinou Eutichia Vaggelatou |
| |
Institution: | (1) Department of Mathematics, University of Athens, Panepistimiopolis, 15784 Athens, Greece |
| |
Abstract: | We consider a sequence X
1, ..., X
n of r.v.'s generated by a stationary Markov chain with state space A = {0, 1, ..., r}, r 1. We study the overlapping appearances of runs of k
i consecutive i's, for all i = 1, ..., r, in the sequence X
1,..., X
n. We prove that the number of overlapping appearances of the above multiple runs can be approximated by a Compound Poisson r.v. with compounding distribution a mixture of geometric distributions. As an application of the previous result, we introduce a specific Multiple-failure mode reliability system with Markov dependent components, and provide lower and upper bounds for the reliability of the system. |
| |
Keywords: | Multiple runs Stein-Chen method Kolmogorov distance Compound Poisson approximation consecutive-k
1 k
r-out-of-n: MFM system |
本文献已被 SpringerLink 等数据库收录! |
|