Success runs in a sequence of exchangeable binary trials
Makaleler > Tam Makale · 2007
Yazarlar: Serkan ERYILMAZ, Sevcan DEMİR ATALAY
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, SCI Expanded İndekslerine Giren Dergi, Uluslararası, 2007, cilt 137, ss 2954-2963
DOI: 10.1016/j.jspi.2006.10.015
Özet
The random variables xi(1), xi(2), are said to be exchangeable (or symmetric) if for each n, P{xi(1) <= x(1), . . ., <= x(n)} = P{xi(pi(1)) <= x(1),...,xi(pi(n)) <= x(n)} for any permutation pi = (pi(1),..., pi(n)) of {1, 2,..., n} and any x(i) is an element of R, i = 1,..., n, i.e. the joint distribution of xi(1), xi(2),...xi(n), is invariant under permutation of its arguments. In this study, run statistics are considered in the situation for which the elements of an exchangeable sequence xi(1), xi(2),...,xi(n) are binary with possible values "I" (success) or "0" (failure). The exact distributions of various run statistics are derived using the fact that the conditional distribution of any run statistic given the number of successes is identical to the corresponding distribution in the independent and identically distributed case. (c) 2007 Elsevier B.V. All rights reserved.