Applications of characteristic functions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Griffin
1964
|
| Schriftenreihe: | Griffin's statistical monographs and courses
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 202 S. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804117205742256128 |
|---|---|
| adam_text | CONTENTS
Chapter Page
1 INTRODUCTION 9
1.1 Random variables and random vectors 9
1.2 Classification of distribution functions 12
1.3 Functions of random variables and random vectors 14
1.4 Expectations 16
1.5 Characteristic functions (univariate case) 19
1.6 Characteristic functions (multivariate case) 22
2 IMPORTANT MULTIVARIATE DISTRIBUTIONS 27
2.1 The multivariate normal distribution 27
2.2 The multinomial distribution 31
2.3 The multivariate negative binomial distribution 36
2.4 The multivariate Poisson distribution 39
2.5 Multivariate Gamma type distributions 40
3 THE DISTRIBUTION PROBLEM OF STATISTICS 44
3.1 The arithmetic and the geometric mean 44
3.2 Distribution problems in univariate normal populations 48
3.3 The distribution of the quotient of certain random variables 56
3.4 Problems leading to chi square and non central chi square distributions 64
3.5 Distribution problems in multivariate populations 66
4 INDEPENDENT STATISTICS IN A GIVEN POPULATION 70
4.1 Linear and quadratic statistics 70
4.2 Uncorrelated and independent statistics 72
4.3 The decomposition of chi squares 72
4.4 Translation invariant and scale invariant statistics 73
5 CHARACTERIZATION OF POPULATIONS BY THE
INDEPENDENCE OF STATISTICS 75
5.1 The independence of two linear forms 75
5.2 Linear and quadratic statistics 79
5.3 The independence of polynomials 82
5.4 Characterization by the independence of the mean and a translation
or scale invariant statistic 101
6 REGRESSION PROBLEMS 103
6.1 Polynomial regression 103
6.2 Constant regression 104
6.3 Linear structural relations 117
7 SOME PROBLEMS IN THE THEORY OF STOCHASTIC
PROCESSES 127
7.1 Characterizations of the Wiener process 127
8
Chapter Page
8 IDENTICALLY DISTRIBUTED STATISTICS 133
8.1 Independently and identically distributed statistics 133
8.2 Identically distributed linear statistics—a theorem of Marcinkiewicz 134
8.3 Identically distributed linear statistics—theorems of Linnik 137
9 CHARACTERIZATION OF POPULATIONS BY THE
DISTRIBUTION OF A STATISTIC 147
9.1 Distribution of a linear statistic specified 147
9.2 A characterization of symmetric stable distributions 148
10 STABILITY THEOREMS 150
10.1 A stability theorem for the Normal family 151
10.2 A stability theorem for the Poisson family 160
Appendix
A. SOME BASIC CONCEPTS OF PROBABILITY THEORY 171
A.1 The probability space 171
A. 2 Random variables and random vectors 172
A. 3 Functions of random variables 174
A.4 Expectations 174
B. FOURIER TRANSFORMS OF PROBABILITY MEASURES ;
IN Rn 177
B.I Some auxiliary theorems 177
B.2 Continuity theorem in Rn 178
C. SOME RESULTS CONCERNING DETERMINANTS AND
MATRICES 180
D. PROOF OF A LEMMA USED IN CHAPTER 3 185
E. PROOF OF LEMMAS USED IN CHAPTER 5 187
F. STOCHASTIC CONVERGENCE 189
F.I Convergence in probability 189
F.2 Convergence in quadratic mean 191
F.3 Convergence almost everywhere 192
F.4 Stochastic integrals 192
References 194
Index 199
|
| any_adam_object | 1 |
| author | Lukacs, Eugene 1906-1987 Laha, R. G. 1930-1999 |
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| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV002911393 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:50:42Z |
| institution | BVB |
| language | English |
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| oclc_num | 31511298 |
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| physical | 202 S. |
| publishDate | 1964 |
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| publisher | Griffin |
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| series | Griffin's statistical monographs and courses |
| series2 | Griffin's statistical monographs and courses |
| spelling | Lukacs, Eugene 1906-1987 Verfasser (DE-588)128913770 aut Applications of characteristic functions E. Lukacs and R. G. Laha London Griffin 1964 202 S. txt rdacontent n rdamedia nc rdacarrier Griffin's statistical monographs and courses 14 Funciones Functions Mathematical statistics Anwendung (DE-588)4196864-5 gnd rswk-swf Charakteristische Funktion (DE-588)4147574-4 gnd rswk-swf Charakteristische Funktion (DE-588)4147574-4 s Anwendung (DE-588)4196864-5 s DE-604 Laha, R. G. 1930-1999 Verfasser (DE-588)124266565X aut Griffin's statistical monographs and courses 14 (DE-604)BV000725110 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001822808&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lukacs, Eugene 1906-1987 Laha, R. G. 1930-1999 Applications of characteristic functions Griffin's statistical monographs and courses Funciones Functions Mathematical statistics Anwendung (DE-588)4196864-5 gnd Charakteristische Funktion (DE-588)4147574-4 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4147574-4 |
| title | Applications of characteristic functions |
| title_auth | Applications of characteristic functions |
| title_exact_search | Applications of characteristic functions |
| title_full | Applications of characteristic functions E. Lukacs and R. G. Laha |
| title_fullStr | Applications of characteristic functions E. Lukacs and R. G. Laha |
| title_full_unstemmed | Applications of characteristic functions E. Lukacs and R. G. Laha |
| title_short | Applications of characteristic functions |
| title_sort | applications of characteristic functions |
| topic | Funciones Functions Mathematical statistics Anwendung (DE-588)4196864-5 gnd Charakteristische Funktion (DE-588)4147574-4 gnd |
| topic_facet | Funciones Functions Mathematical statistics Anwendung Charakteristische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001822808&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000725110 |
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