On Success Runs in a Sequence of Dependent Trials With a Change Point

Abstract

Let {X-i}(i=1)(n) be a sequence of n dependent binary trials such that the first n(1) in {X-i}(i=1)(n) are of type 1 and follow an exchangeable joint distribution denoted by L-1, and the last n2 elements in {X-i}(i=1)(n) are of type 2 and follow an exchangeable joint distribution denoted by L-2, where n(1) + n(2) = n. That is, the trials within the same group are exchangeable dependent, and the trials in different groups are dependent in a general sense. The exact distributions of the number of success runs of length k in {X-i}(i=1)(n) are obtained under nonoverlapping and at least schemes. (C) 2017 Elsevier B.V. All rights reserved.