Unimodality of probability measures:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Mathematics and its applications
382 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 251 S. |
| ISBN: | 0792343182 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface xi
1 Prelude 1
1.1 Notations 1
1.2 Radon measures and strict topology 3
1.3 Convexity and boundaries 8
1.4 Transforms and convolutions 11
1.5 Miscellany 14
1.5.1 Quasi concave functions 14
1.5.2 Convex functions 16
1.5.3 Correspondences 16
2 Khinchin structures 19
2.1 Representing measures 20
2.2 Choquet representation 26
2.3 Khinchin spaces 30
2.4 Khinchin morphisms 34
2.5 Standard Khinchin spaces 39
2.6 Other forms of the Theorem of Khinchin 44
2.7 Khinchin structures on groups 47
2.8 Comments 52
3 Concepts of unimodality 55
3.1 Beta unimodality 55
3.1.1 Construction of the Khinchin space 56
3.1.2 Characterizations of beta unimodality 62
3.1.3 Further properties of beta unimodality 65
3.1.4 (a, 1) and (1, ^ unimodality 70
3.1.5 Examples 72
3.2 Block Beta unimodality 74
3.3 Some more concepts of unimodality 75
3.3.1 Central convex unimodality 77
3.3.2 Monotone unimodality 87
3.3.3 Linear unimodality 87
3.3.4 Schur unimodality 88
vii
viii CONTENTS
3.3.5 Closed convex sets of star unimodal probability
measures 95
3.4 Simulation of Khinchin probability measures 104
3.5 Comments 108
4 Khinchin s classical unimodality 111
4.1 Single humped probability density functions Ill
4.1.1 Characterization property 112
4.1.2 Iteratively single humped functions 114
4.1.3 Maximum likelihood estimators 118
4.2 Concentration functions 123
4.2.1 Characterization property 125
4.2.2 A representation theorem 128
4.2.3 Location, dispersion, skewness 133
4.3 Preserving unimodality by mixing 136
4.4 Comments 138
5 Discrete unimodality 143
5.1 Unimodality on the set of all integers 143
5.1.1 Several definitions 143
5.1.2 The mean median mode inequality 148
5.1.3 Variance upper and lower bounds 151
5.1.4 Mixing discrete distributions 154
5.1.5 Concentration functions 159
5.2 A one parameter class of random variables 166
5.3 A two parameter class of random variables 168
5.3.1 Preliminaries 169
5.3.2 Basic properties 171
5.3.3 Further properties 175
5.4 Comments 179
6 Strong unimodality 183
6.1 Strong unimodality, logconcavity, and dispersivity 183
6.2 Multiplicative strong unimodality 190
6.3 Discrete strong unimodality 198
6.4 Comments 199
7 Positivity of functional moments 201
7.1 Problem 234 201
7.2 Mean preserving representations 202
7.2.1 General representations 203
7.2.2 Specific representations 206
7.2.3 Characterization property 211
7.3 Slantedness 215
7.3.1 Main tools 215
7.3.2 Conditions for slantedness 217
CONTENTS ix
7.3.3 Signed moments 220
7.3.4 About the concept of slantedness 220
7.4 Comments 222
Bibliography 225
Symbol index 241
Name index 243
Subject index 247
|
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| author | Bertin, Emile M. J. Cuculescu, Ioan Theodorescu, Radu |
| author_facet | Bertin, Emile M. J. Cuculescu, Ioan Theodorescu, Radu |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:07:45Z |
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| isbn | 0792343182 |
| language | English |
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| physical | XIV, 251 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Bertin, Emile M. J. Verfasser aut Unimodality of probability measures by Emile M. J. Bertin, Ioan Cuculescu and Radu Theodorescu Dordrecht [u.a.] Kluwer 1997 XIV, 251 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 382 Probability measures Theory of distributions (Functional analysis) Choquet-Kapazität (DE-588)4425296-1 gnd rswk-swf Choquet-Kapazität (DE-588)4425296-1 s DE-604 Cuculescu, Ioan Verfasser aut Theodorescu, Radu Verfasser aut Mathematics and its applications 382 (DE-604)BV008163334 382 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007605736&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertin, Emile M. J. Cuculescu, Ioan Theodorescu, Radu Unimodality of probability measures Mathematics and its applications Probability measures Theory of distributions (Functional analysis) Choquet-Kapazität (DE-588)4425296-1 gnd |
| subject_GND | (DE-588)4425296-1 |
| title | Unimodality of probability measures |
| title_auth | Unimodality of probability measures |
| title_exact_search | Unimodality of probability measures |
| title_full | Unimodality of probability measures by Emile M. J. Bertin, Ioan Cuculescu and Radu Theodorescu |
| title_fullStr | Unimodality of probability measures by Emile M. J. Bertin, Ioan Cuculescu and Radu Theodorescu |
| title_full_unstemmed | Unimodality of probability measures by Emile M. J. Bertin, Ioan Cuculescu and Radu Theodorescu |
| title_short | Unimodality of probability measures |
| title_sort | unimodality of probability measures |
| topic | Probability measures Theory of distributions (Functional analysis) Choquet-Kapazität (DE-588)4425296-1 gnd |
| topic_facet | Probability measures Theory of distributions (Functional analysis) Choquet-Kapazität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007605736&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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