Browsing by Author "Kemalbay, Gulder"

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Citation - WoS: 8
Citation - Scopus: 6
Joint Distribution of New Sample Rank of Bivariate Order Statistics
(Taylor & Francis Ltd, 2015) Kemalbay, Gulder; Bayramoğlu, İsmihan
Let (X-k, Y-k), k = 1, 2,..., n, be independent copies of bivariate random vector (X, Y) with joint cumulative distribution function F(x, y) and probability density function f (x, y). For 1 = r, s = n, the vector of order statistics of X1: n = X2: n = = Xn: n and Y1: n = Y2: n = = Yn: n, respectively, is denoted by (Xr: n, Ys: n). Let (Xn+ i, Yn+ i), i = 1, 2,..., m, be a new sample from F(x, y), which is independent from (Xk, Yk), k = 1, 2,..., n. Let.1 be the rank of order statistics Xr: n in a new sample Xn+ 1, Xn+ 2,..., Xn+ m and.2 be the rank of order statistics Ys: n in a new sample Yn+ 1, Yn+ 2,..., Yn+ m. We derive the joint distribution of discrete random vector (.1,.2) and a general scheme wherein the distributions of new and old samples are different is considered. Numerical examples for given well- known distribution are also provided.
Citation - WoS: 2
Citation - Scopus: 1
On Distribution of Upper Marginal Records in Bivariate Random Sequences
(Scientific Technical Research Council Turkey-Tubitak, 2019) Kemalbay, Gulder; Bayramoğlu, İsmihan
The theory of record values has been extensively studied in the statistical literature. However, there are not many papers devoted to the theory of records for bivariate and multivariate random sequences. This paper presents the marginal record values and record times in extended sequence of bivariate random vectors. The joint distributions of some upper marginal records are derived. Some results on joint probability mass function of upper record time vectors and distribution function of upper record value vectors are given via copula functions. Moreover, the numerical and graphical applications of considered upper records using flood data and prediction of rainfall variables such as intensity, depth, and duration are provided.
Citation - WoS: 7
Citation - Scopus: 10
Some Novel Discrete Distributions Under Fourfold Sampling Schemes and Conditional Bivariate Order Statistics
(Elsevier Science Bv, 2013) Bayramoğlu, İsmihan; Kemalbay, Gulder
This paper presents some novel trivariate discrete distributions that are obtained by modifying the bivariate binomial distribution. These distributions are important probability models for the development of conditional bivariate order statistics. The distributional properties of bivariate order statistics are studied and derived under the condition that certain values of the underlying random vectors (X, Y) are truncated and fall in the threshold set {(t, s) is an element of R-2 : t <= u, s <= u}, (u, v) is an element of R-2. (C) 2013 Elsevier B.V. All rights reserved.