Abstract

The paper presents the estimate for the total variation distance between the distribution of the number of appearances of homogeneous disjoint events in a segment of strongly ergodic Markov chain on the finite state space and accompanying Poisson distribution (i.e., Poisson distribution with a parameter equal to the expectation of the random variable under consideration). For this purpose the Chen-Stein method was used. As a result Poisson and normal limit theorems for the number of events appearances are derived. The considered scheme describes the well-known number of runs on consecutive letters, the number of -recurrent runs, etc., and can be used for describing the properties of distribution of the special form scan statistic.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 3
Year: 2019

DOI: 10.12732/ijam.v32i3.13

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