Sums, Trimmed Sums and Extremes:
Gespeichert in:
| Weitere Verfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1991
|
| Schriftenreihe: | Progress in Probability
23 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The past decade has seen a resurgence of interest in the study of the asymptotic behavior of sums formed from an independent sequence of random variables. In particular, recent attention has focused on the interaction of the extreme summands with, and their influence upon, the sum. As observed by many authors, the limit theory for sums can be meaningfully expanded far beyond the scope of the classical theory if an "intermediate" portion (i. e. , an unbounded number but a vanishingly small proportion) of the extreme summands in the sum are deleted or otherwise modified ("trimmed"). The role of the normal law is magnified in these intermediate trimmed theories in that most or all of the resulting limit laws involve variance-mixtures of normals. The objective of this volume is to present the main approaches to this study of intermediate trimmed sums which have been developed so far, and to illustrate the methods with a variety of new results. The presentation has been divided into two parts. Part I explores the approaches which have evolved from classical analytical techniques (conditioning, Fourier methods, symmetrization, triangular array theory). Part II is used on the quantile transform technique and utilizes weak and strong approximations to uniform empirical process. The analytic approaches of Part I are represented by five articles involving two groups of authors |
| Beschreibung: | 1 Online-Ressource (X, 418 p) |
| ISBN: | 9781468467932 9781468467956 |
| DOI: | 10.1007/978-1-4684-6793-2 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804153093838864384 |
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| any_adam_object | |
| author2 | Hahn, Marjorie G. Mason, David M. Weiner, Daniel C. |
| author2_role | edt edt edt |
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| dewey-search | 515.24 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| format | Electronic eBook |
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| id | DE-604.BV042421120 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468467932 9781468467956 |
| language | English |
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| series | Progress in Probability |
| series2 | Progress in Probability |
| spelling | Hahn, Marjorie G. edt Sums, Trimmed Sums and Extremes edited by Marjorie G. Hahn, David M. Mason, Daniel C. Weiner Boston, MA Birkhäuser Boston 1991 1 Online-Ressource (X, 418 p) txt rdacontent c rdamedia cr rdacarrier Progress in Probability 23 The past decade has seen a resurgence of interest in the study of the asymptotic behavior of sums formed from an independent sequence of random variables. In particular, recent attention has focused on the interaction of the extreme summands with, and their influence upon, the sum. As observed by many authors, the limit theory for sums can be meaningfully expanded far beyond the scope of the classical theory if an "intermediate" portion (i. e. , an unbounded number but a vanishingly small proportion) of the extreme summands in the sum are deleted or otherwise modified ("trimmed"). The role of the normal law is magnified in these intermediate trimmed theories in that most or all of the resulting limit laws involve variance-mixtures of normals. The objective of this volume is to present the main approaches to this study of intermediate trimmed sums which have been developed so far, and to illustrate the methods with a variety of new results. The presentation has been divided into two parts. Part I explores the approaches which have evolved from classical analytical techniques (conditioning, Fourier methods, symmetrization, triangular array theory). Part II is used on the quantile transform technique and utilizes weak and strong approximations to uniform empirical process. The analytic approaches of Part I are represented by five articles involving two groups of authors Mathematics Sequences (Mathematics) Distribution (Probability theory) Sequences, Series, Summability Probability Theory and Stochastic Processes Mathematik Summe (DE-588)4193845-8 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Zufällige Folge (DE-588)4191092-8 gnd rswk-swf Summierbarkeit (DE-588)4294383-8 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 s Summe (DE-588)4193845-8 s Grenzwertsatz (DE-588)4158163-5 s 1\p DE-604 Asymptotische Methode (DE-588)4287476-2 s 2\p DE-604 Summierbarkeit (DE-588)4294383-8 s 3\p DE-604 Zufällige Folge (DE-588)4191092-8 s 4\p DE-604 Mason, David M. edt Weiner, Daniel C. edt Progress in Probability 23 (DE-604)BV004163567 23 https://doi.org/10.1007/978-1-4684-6793-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sums, Trimmed Sums and Extremes Progress in Probability Mathematics Sequences (Mathematics) Distribution (Probability theory) Sequences, Series, Summability Probability Theory and Stochastic Processes Mathematik Summe (DE-588)4193845-8 gnd Asymptotische Methode (DE-588)4287476-2 gnd Zufällige Folge (DE-588)4191092-8 gnd Summierbarkeit (DE-588)4294383-8 gnd Grenzwertsatz (DE-588)4158163-5 gnd Zufallsvariable (DE-588)4129514-6 gnd |
| subject_GND | (DE-588)4193845-8 (DE-588)4287476-2 (DE-588)4191092-8 (DE-588)4294383-8 (DE-588)4158163-5 (DE-588)4129514-6 |
| title | Sums, Trimmed Sums and Extremes |
| title_auth | Sums, Trimmed Sums and Extremes |
| title_exact_search | Sums, Trimmed Sums and Extremes |
| title_full | Sums, Trimmed Sums and Extremes edited by Marjorie G. Hahn, David M. Mason, Daniel C. Weiner |
| title_fullStr | Sums, Trimmed Sums and Extremes edited by Marjorie G. Hahn, David M. Mason, Daniel C. Weiner |
| title_full_unstemmed | Sums, Trimmed Sums and Extremes edited by Marjorie G. Hahn, David M. Mason, Daniel C. Weiner |
| title_short | Sums, Trimmed Sums and Extremes |
| title_sort | sums trimmed sums and extremes |
| topic | Mathematics Sequences (Mathematics) Distribution (Probability theory) Sequences, Series, Summability Probability Theory and Stochastic Processes Mathematik Summe (DE-588)4193845-8 gnd Asymptotische Methode (DE-588)4287476-2 gnd Zufällige Folge (DE-588)4191092-8 gnd Summierbarkeit (DE-588)4294383-8 gnd Grenzwertsatz (DE-588)4158163-5 gnd Zufallsvariable (DE-588)4129514-6 gnd |
| topic_facet | Mathematics Sequences (Mathematics) Distribution (Probability theory) Sequences, Series, Summability Probability Theory and Stochastic Processes Mathematik Summe Asymptotische Methode Zufällige Folge Summierbarkeit Grenzwertsatz Zufallsvariable |
| url | https://doi.org/10.1007/978-1-4684-6793-2 |
| volume_link | (DE-604)BV004163567 |
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