The Normal Distribution: Characterizations with Applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1995
|
| Schriftenreihe: | Lecture Notes in Statistics
100 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3 |
| Beschreibung: | 1 Online-Ressource (VIII, 139p) |
| ISBN: | 9781461225607 9780387979908 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4612-2560-7 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042420046 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1995 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461225607 |c Online |9 978-1-4612-2560-7 | ||
| 020 | |a 9780387979908 |c Print |9 978-0-387-97990-8 | ||
| 024 | 7 | |a 10.1007/978-1-4612-2560-7 |2 doi | |
| 035 | |a (OCoLC)863773607 | ||
| 035 | |a (DE-599)BVBBV042420046 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 519.2 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Bryc, Wlodzimierz |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Normal Distribution |b Characterizations with Applications |c by Wlodzimierz Bryc |
| 264 | 1 | |a New York, NY |b Springer New York |c 1995 | |
| 300 | |a 1 Online-Ressource (VIII, 139p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Lecture Notes in Statistics |v 100 |x 0930-0325 | |
| 500 | |a This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Normalverteilung |0 (DE-588)4075494-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Normalverteilung |0 (DE-588)4075494-7 |D s |
| 689 | 0 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-2560-7 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027855463 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153091441819648 |
|---|---|
| any_adam_object | |
| author | Bryc, Wlodzimierz |
| author_facet | Bryc, Wlodzimierz |
| author_role | aut |
| author_sort | Bryc, Wlodzimierz |
| author_variant | w b wb |
| building | Verbundindex |
| bvnumber | BV042420046 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863773607 (DE-599)BVBBV042420046 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2560-7 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02992nmm a2200481zcb4500</leader><controlfield tag="001">BV042420046</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1995 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461225607</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-2560-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387979908</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-97990-8</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-2560-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863773607</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420046</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bryc, Wlodzimierz</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Normal Distribution</subfield><subfield code="b">Characterizations with Applications</subfield><subfield code="c">by Wlodzimierz Bryc</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VIII, 139p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Lecture Notes in Statistics</subfield><subfield code="v">100</subfield><subfield code="x">0930-0325</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probability Theory and Stochastic Processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Normalverteilung</subfield><subfield code="0">(DE-588)4075494-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Normalverteilung</subfield><subfield code="0">(DE-588)4075494-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-2560-7</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027855463</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV042420046 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461225607 9780387979908 |
| issn | 0930-0325 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855463 |
| oclc_num | 863773607 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VIII, 139p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Lecture Notes in Statistics |
| spelling | Bryc, Wlodzimierz Verfasser aut The Normal Distribution Characterizations with Applications by Wlodzimierz Bryc New York, NY Springer New York 1995 1 Online-Ressource (VIII, 139p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 100 0930-0325 This book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3 Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Normalverteilung (DE-588)4075494-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Normalverteilung (DE-588)4075494-7 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-2560-7 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 |
| spellingShingle | Bryc, Wlodzimierz The Normal Distribution Characterizations with Applications Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Normalverteilung (DE-588)4075494-7 gnd |
| subject_GND | (DE-588)4075494-7 (DE-588)4123623-3 |
| title | The Normal Distribution Characterizations with Applications |
| title_auth | The Normal Distribution Characterizations with Applications |
| title_exact_search | The Normal Distribution Characterizations with Applications |
| title_full | The Normal Distribution Characterizations with Applications by Wlodzimierz Bryc |
| title_fullStr | The Normal Distribution Characterizations with Applications by Wlodzimierz Bryc |
| title_full_unstemmed | The Normal Distribution Characterizations with Applications by Wlodzimierz Bryc |
| title_short | The Normal Distribution |
| title_sort | the normal distribution characterizations with applications |
| title_sub | Characterizations with Applications |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Normalverteilung (DE-588)4075494-7 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Normalverteilung Lehrbuch |
| url | https://doi.org/10.1007/978-1-4612-2560-7 |
| work_keys_str_mv | AT brycwlodzimierz thenormaldistributioncharacterizationswithapplications |