Asymptotic Law of the jth Records in the Bivariate Exponential Case
We consider a sequence (Xi,Yi)1⩽i⩽n of independent and identically distributed random variables with joint cumulative distribution H(x,y), which has exponential marginals F(x) and G(y) with parameter λ=1. We also assume that Xi(ω)≠Yi(ω), ∀i∈N, and ω∈Ω. We denote Rk(j)k⩾1 and Sk(j)k⩾1 by the sequen...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/458914 |
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| author | Grine Azedine |
| author_facet | Grine Azedine |
| author_sort | Grine Azedine |
| collection | DOAJ |
| description | We consider a sequence (Xi,Yi)1⩽i⩽n of independent and identically distributed random variables with joint cumulative distribution H(x,y), which has exponential marginals F(x) and G(y) with parameter λ=1. We also assume that Xi(ω)≠Yi(ω), ∀i∈N, and ω∈Ω. We denote Rk(j)k⩾1 and Sk(j)k⩾1 by the sequences of the jth records in the sequences (Xi)1⩽i⩽n, (Yi)1⩽i⩽n, respectively. The main result of of the paper is to prove the asymptotic independence of Rk(j)k⩾1 and Sk(j)k⩾1 using the property of stopping time of the jth record times and that of the exponential distribution. |
| format | Article |
| id | doaj-art-643f453bd99145668f4d2b9ee5fe6f1f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-643f453bd99145668f4d2b9ee5fe6f1f2025-02-03T06:12:31ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/458914458914Asymptotic Law of the jth Records in the Bivariate Exponential CaseGrine Azedine0Department of Mathematics, College of Science, Al-Imam Muhammad Ibn Saud Islamic University, P.O. Box 90950, Riyadh 11623, Saudi ArabiaWe consider a sequence (Xi,Yi)1⩽i⩽n of independent and identically distributed random variables with joint cumulative distribution H(x,y), which has exponential marginals F(x) and G(y) with parameter λ=1. We also assume that Xi(ω)≠Yi(ω), ∀i∈N, and ω∈Ω. We denote Rk(j)k⩾1 and Sk(j)k⩾1 by the sequences of the jth records in the sequences (Xi)1⩽i⩽n, (Yi)1⩽i⩽n, respectively. The main result of of the paper is to prove the asymptotic independence of Rk(j)k⩾1 and Sk(j)k⩾1 using the property of stopping time of the jth record times and that of the exponential distribution.http://dx.doi.org/10.1155/2014/458914 |
| spellingShingle | Grine Azedine Asymptotic Law of the jth Records in the Bivariate Exponential Case Journal of Mathematics |
| title | Asymptotic Law of the jth Records in the Bivariate Exponential Case |
| title_full | Asymptotic Law of the jth Records in the Bivariate Exponential Case |
| title_fullStr | Asymptotic Law of the jth Records in the Bivariate Exponential Case |
| title_full_unstemmed | Asymptotic Law of the jth Records in the Bivariate Exponential Case |
| title_short | Asymptotic Law of the jth Records in the Bivariate Exponential Case |
| title_sort | asymptotic law of the jth records in the bivariate exponential case |
| url | http://dx.doi.org/10.1155/2014/458914 |
| work_keys_str_mv | AT grineazedine asymptoticlawofthejthrecordsinthebivariateexponentialcase |