Joint distribution of new sample rank of bivariate order statistics

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KEMALBAY G., Bayramoglu (Bairamov) I.

JOURNAL OF APPLIED STATISTICS, vol.42, no.10, pp.2280-2289, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 10
  • Publication Date: 2015
  • Doi Number: 10.1080/02664763.2015.1023705
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2280-2289
  • Yıldız Technical University Affiliated: Yes


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.