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ON AN EXAMPLE OF SUMS OF PAIRWISE INDEPENDENT RANDOM VARIABLES FOR WHICH THE CENTRAL LIMIT THEOREM HOLDS
http://hdl.handle.net/10131/5682
http://hdl.handle.net/10131/56821afc53c2-6f5f-4a2b-a367-74501aeef837
名前 / ファイル | ライセンス | アクション |
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YMJ_45_N2_1998_087-096.pdf (689.4 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2009-12-15 | |||||
タイトル | ||||||
タイトル | ON AN EXAMPLE OF SUMS OF PAIRWISE INDEPENDENT RANDOM VARIABLES FOR WHICH THE CENTRAL LIMIT THEOREM HOLDS | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Krajka, Andrzej
× Krajka, Andrzej |
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著者所属 | ||||||
Institute of Mathematics, Maria Curie-Sklodowska University, Pl. Marii Curie-Sklodowskiej 1, 20-031 Lublin, POLAND | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Let $¥{X_{n)}n¥geq 1¥}$ be a sequence of symmetric pairwise independent and identically distributed (piid) random variables. If $EX_{1}=0,$ $EX_{1}^{2}=1$ , then the Central Limit Theorem (CLT) is proved by Dug Hun Hong [5]. In this paper we show that under the above assumptions the sequence so defined is a sequence of martingale differences and CLT follows from McLeish's result. The class of pairwise independent random variables for which CLT holds, described in [5], is in consequence the known class of martingale differences. Furthermore, the assumption of pairwise independency is not crucial there and may be weakened. It seems that the assumption of pairwise independency is not essential in CLT, but we give an interesting result in this direction. Furthermore, an example is provided to illustrate this result. | |||||
書誌情報 |
Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学 巻 45, 号 2, p. 87-96, 発行日 1998 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00440523 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0089285X | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
出版者 | ||||||
出版者 | Yokohama City University and Yokohama National University |