Browsing by Author "Demir, Sevcan"

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Citation - WoS: 17
Citation - Scopus: 20
Run Statistics in a Sequence of Arbitrarily Dependent Binary Trials
(Springer, 2010) Demir, Sevcan; Eryılmaz, Serkan
Let {Z (i) } (ia parts per thousand yen1) be an arbitrary sequence of trials with two possible outcomes either success (1) or failure (0). General expressions for the exact distributions of runs, both success and failure, in Z (1), . . . , Z (n) are presented. Our method is based on the use of joint distribution of success and failure run lengths and unifies the results on distribution of runs. As a special case of our results we obtain the distributions of runs for various binary sequences. As illustrated in the paper the results enable us to derive the distribution of runs for binary trials arising in urn models.
Citation - WoS: 44
Citation - Scopus: 45
Success Runs in a Sequence of Exchangeable Binary Trials
(Elsevier Science Bv, 2007) Eryılmaz, Serkan; Demir, Sevcan
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.