Limit Theory for Joint Generalized Order Statistics
In Kamps [7] generalized order statistics (gos) have been introduced as a unifying theme for several models of ascendingly ordered random variables (rv’s). The main aim of this paper is to study the limit joint distribution function (df) of any two statistics in a wide subclass of the gos model kno...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Instituto Nacional de Estatística | Statistics Portugal
2014-12-01
|
| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/151 |
| _version_ | 1817999428885151744 |
|---|---|
| author | H.M. Barakat E.M. Nigm M.A. Abd Elgawad |
| author_facet | H.M. Barakat E.M. Nigm M.A. Abd Elgawad |
| author_sort | H.M. Barakat |
| collection | DOAJ |
| description |
In Kamps [7] generalized order statistics (gos) have been introduced as a unifying theme for several models of ascendingly ordered random variables (rv’s). The main aim of this paper is to study the limit joint distribution function (df) of any two statistics in a wide subclass of the gos model known as m-gos. This subclass contains many important practical models of gos such as ordinary order statistics (oos), order statistics with non-integer sample size, and sequential order statistics (sos). The limit df’s of lower-lower extreme, upper-upper extreme, lower-upper extreme, centralcentral and lower-lower intermediate m-gos are obtained. It is revealed that the convergence of the marginals m-gos implies the convergence of the joint df. Moreover, the conditions, under which the asymptotic independence between the two marginals occurs, are derived.
|
| first_indexed | 2024-04-14T03:08:49Z |
| format | Article |
| id | doaj.art-de8489c6f8f349268d889e81dd21b06f |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T03:08:49Z |
| publishDate | 2014-12-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-de8489c6f8f349268d889e81dd21b06f2022-12-22T02:15:39ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712014-12-0112310.57805/revstat.v12i3.151Limit Theory for Joint Generalized Order StatisticsH.M. Barakat 0E.M. Nigm 1M.A. Abd Elgawad 2Zagazig UniversityZagazig University Benha University In Kamps [7] generalized order statistics (gos) have been introduced as a unifying theme for several models of ascendingly ordered random variables (rv’s). The main aim of this paper is to study the limit joint distribution function (df) of any two statistics in a wide subclass of the gos model known as m-gos. This subclass contains many important practical models of gos such as ordinary order statistics (oos), order statistics with non-integer sample size, and sequential order statistics (sos). The limit df’s of lower-lower extreme, upper-upper extreme, lower-upper extreme, centralcentral and lower-lower intermediate m-gos are obtained. It is revealed that the convergence of the marginals m-gos implies the convergence of the joint df. Moreover, the conditions, under which the asymptotic independence between the two marginals occurs, are derived. https://revstat.ine.pt/index.php/REVSTAT/article/view/151generalized order statisticsgeneralized extreme order statisticsgeneralized central order statisticsgeneralized intermediate order statistics |
| spellingShingle | H.M. Barakat E.M. Nigm M.A. Abd Elgawad Limit Theory for Joint Generalized Order Statistics Revstat Statistical Journal generalized order statistics generalized extreme order statistics generalized central order statistics generalized intermediate order statistics |
| title | Limit Theory for Joint Generalized Order Statistics |
| title_full | Limit Theory for Joint Generalized Order Statistics |
| title_fullStr | Limit Theory for Joint Generalized Order Statistics |
| title_full_unstemmed | Limit Theory for Joint Generalized Order Statistics |
| title_short | Limit Theory for Joint Generalized Order Statistics |
| title_sort | limit theory for joint generalized order statistics |
| topic | generalized order statistics generalized extreme order statistics generalized central order statistics generalized intermediate order statistics |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/151 |
| work_keys_str_mv | AT hmbarakat limittheoryforjointgeneralizedorderstatistics AT emnigm limittheoryforjointgeneralizedorderstatistics AT maabdelgawad limittheoryforjointgeneralizedorderstatistics |