Browsing by Author "Bairamov, I."

Now showing 1 - 3 of 3

Citation - WoS: 4
Citation - Scopus: 3
Number of Observations Near the Maximum in an F-Alpha
(Taylor & Francis Ltd, 2013) Bairamov, I.; Stepanov, A.
Let K n (a) be the number of observations in the interval (M n ,-a, M n ), where M n is the maximum value in a sequence of size n. We study the asymptotic properties of K n (a) under the F a-scheme and discuss the influence of the associated sequence a n on the limit behaviour of this random variable.
Citation - WoS: 20
Citation - Scopus: 22
Numbers of Near Bivariate Record-Concomitant Observations
(Elsevier Inc, 2011) Bairamov, I.; Stepanov, A.
Let (Z) over bar (1) = (X(1), Y(1)), (Z) over bar (2) = (X(2), Y(2)), ... be independent and identically distributed random vectors with continuous distribution. Let L(n) and X (n) denote the nth record time and the nth record value obtained from the sequence of Xs. Let Y(n) denote the concomitant of the nth record value, which relates to the sequence of Ys. We call (Z) over bar (i) a near bivariate nth record-concomitant observation if (Z) over bar (i) belongs to the open rectangle (X (n) - a, X (n)) x (Y(n) - b(1), Y(n) b(2)), where a, b(1), b(2) > 0 and L(n) < i < L(n + 1). Asymptotic properties of the numbers of near bivariate record-concomitant observations are discussed in the present work. New techniques for generating bivariate record-concomitants, the numbers of near record observations and the numbers of near bivariate record-concomitant observations are also proposed. (c) 2011 Elsevier Inc. All rights reserved.
Citation - WoS: 10
Citation - Scopus: 10
Numbers of Near-Maxima for the Bivariate Case
(Elsevier, 2010) Bairamov, I.; Stepanov, A.
Let (Z) over bar (1) = (X-1, Y-1)....(Z) over bar (n) = (X-n, Y-n) be independent and identically distributed random vectors with continuous distribution. Let K-n(a, b(1), b(2)) be the number of sample elements that belong to the open rectangle (X-max((n)) - a, X-max((n))) x (Y-max((n)) - b(1), Y-max((n)) + b(2)) - numbers of near-maxima in the bivariate case. in the present paper, we discuss asymptotic properties of K-n (a, b(1), b(2)) and K-n(infinity, 0, infinity). (C) 2009 Elsevier B.V. All rights reserved.