On Number of Occurrences of Success Runs of Specified Length in a Higher-Order Two-State Markov Chain

In this: publication
By this: publisher
In this Subject: <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: Uchida M.

Author: Uchida M.

Source: Annals of the Institute of Statistical Mathematics, Volume 50, Number 3, September 1998 , pp. 587-601(15)

Publisher: Springer

Buy & download fulltext article:

Price: $47.00 plus tax (Refund Policy)

Abstract:

Let X_-m+1, X_-m+2, …, X_0, X_1, X_2, …, X_n be a time-homogeneous {0, 1}-valued m-th order Markov chain. The probability distributions of numbers of runs of "1" of length k (k m) and of "1" of length k (k < m) in the sequence of a {0, 1}-valued m-th order Markov chain are studied. There are some ways of counting numbers of runs with length k. This paper studies the distributions based on four ways of counting numbers of runs, i.e., the number of non-overlapping runs of length k, the number of runs with length greater than or equal to k, the number of overlapping runs of length k and the number of runs of length exactly k.