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Products of random variables: applications to problems of physics and to arithmetical functions

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Bibliographic Details
Main Author:	Galambos, János 1940-2019 (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Marcel Dekker 2004
Series:	Pure and applied mathematics 268
Subjects:	Probabilités Random walks (statistiek) Variables aléatoires Probabilities Random variables Zufallsvariable Wahrscheinlichkeitsrechnung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013161873&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	VI, 323 S.
ISBN:	0824754026

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Record in the Search Index

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adam_text	PRODUCTS OF RANDOM VARIABLES APPLICATIONS TO PROBLEMS OF PHYSICS AND TO ARITHMETICAL FUNCTIONS JANOS GALAMBOS TEMPLE UNIVERSITY PHILADELPHIA, PENNSYLVANIA, U.S.A. ITALO SIMONELLI TEXAS A&M UNIVERSITY COMMERCE, TEXAS, U.S.A. MARCEL MARCEL DEKKER, INC. NEW YORK * BASEL DEKKER CONTENTS PREFACE III 1 FOUNDATIONS 1 1.1 BASIC CONCEPTS AND NOTATION 1 1.1.1 EVENTS AND PROBABILITY 1 1.1.2 RANDOM VARIABLES 3 1.1.3 WEAK CONVERGENCE; CHARACTERISTIC FUNCTIONS . . 6 1.1.4 CONVERGENCE IN PROBABILITY AND ALMOST SURE CON- VERGENCE 8 1.2 ELEMENTARY FORMULAS FOR PRODUCTS 11 1.3 MELLIN TRANSFORM 15 1.4 SYMMETRIC DISTRIBUTIONS 26 1.5 BONFERRONI-TYPE INEQUALITIES 39 1.6 LIMITING DISTRIBUTION OF PRODUCTS 45 2 LIMIT THEOREMS 55 2.1 LOGARITHMICALLY POISSON DISTRIBUTIONS 55 2.2 THE CLASS OF /^-DISTRIBUTIONS FOR PRODUCTS 58 2.3 ABSOLUTE CONVERGENCE OF PRODUCTS 62 2.4 CONDITIONAL DISTRIBUTIONS FOR PRODUCTS 70 2.5 TRIANGULAR ARRAYS 79 2.6 I.I.D. RANDOM VARIABLES 100 2.7 ORDER STATISTICS AS PRODUCTS 103 3 CHARACTERIZATION 111 3.1 GENERAL DESCRIPTION OF CHARACTERIZATION ILL 3.2 THE CAUCHY FUNCTIONAL EQUATION 114 3.3 CHARACTERIZATIONS BY DECOMPOSITIONS 120 3.4 NORMAL AND CAUCHY DISTRIBUTIONS 135 VI CONTENTS 3.5 THE NORMAL DISTRIBUTION 139 3.6 BIVARIATE DISTRIBUTIONS 147 4 INTERACTING PARTICLES 155 4.1 INTRODUCTION 155 4.2 MODELS AND DUAL SYSTEMS 157 4.3 IPS WITH DUAL OF INCREASING SIZE 167 4.4 RANDOM WALKS 188 5 ARITHMETICAL FUNCTIONS 199 5.1 INTRODUCTION 199 5.2 THE KUBILIUS-TURAN INEQUALITY 204 5.3 A THEOREM OF BAKSTYS 213 5.4 DISTRIBUTION OF MULTIPLICATIVE FUNCTIONS 230 5.5 VARIANTS OF A CONJECTURE OF ERDOS 241 5.6 SEQUENCES OF PRIME DIVISORS 243 6 MISCELLANEOUS RESULTS 249 6.1 BINARY VARIABLES 249 6.2 THE SIGN OF A PRODUCT AND MARKOV CHAINS 253 6.3 SEQUENCES OF THE 1 PRIME NUMBERS 257 6.4 HILBERT SPACES 260 6.5 APPLIED MODELS WITH PRODUCTS 267 6.5.1 MODELS RELATED TO INCOME 267 6.5.2 MULTIPLYING OBSERVATIONS FOR SMOOTHING .... 271 6.5.3 ESTIMATION FOR THE PARETO DISTRIBUTION . . . . . 273 6.5.4 PRODUCTS OF BETA RANDOM VARIABLES 274 6.5.5 PRODUCTS OF GAMMA RANDOM VARIABLES 282 6.5.6 RANDOM DISCRIMINANTS 284 6.5.7 NORMALIZED PRODUCTS OF SUMS 286 6.5.8 DISTRIBUTION OF PRODUCTS OF ORDER STATISTICS . . .288 6.5.9 CHARACTERIZATION OF UNIMODALITY VIA PRODUCTS . 293 6.6 QUOTIENTS OF RANDOM VARIABLES 295 BIBLIOGRAPHY 303 AUTHOR INDEX 317 SUBJECT INDEX . 321
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discipline	Physik Mathematik Wirtschaftswissenschaften
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isbn	0824754026
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series	Pure and applied mathematics
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spellingShingle	Galambos, János 1940-2019 Products of random variables applications to problems of physics and to arithmetical functions Pure and applied mathematics Probabilités Random walks (statistiek) gtt Variables aléatoires Probabilities Random variables Zufallsvariable (DE-588)4129514-6 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd
subject_GND	(DE-588)4129514-6 (DE-588)4064324-4
title	Products of random variables applications to problems of physics and to arithmetical functions
title_auth	Products of random variables applications to problems of physics and to arithmetical functions
title_exact_search	Products of random variables applications to problems of physics and to arithmetical functions
title_full	Products of random variables applications to problems of physics and to arithmetical functions Janos Galambos ; Italo Simonelli
title_fullStr	Products of random variables applications to problems of physics and to arithmetical functions Janos Galambos ; Italo Simonelli
title_full_unstemmed	Products of random variables applications to problems of physics and to arithmetical functions Janos Galambos ; Italo Simonelli
title_short	Products of random variables
title_sort	products of random variables applications to problems of physics and to arithmetical functions
title_sub	applications to problems of physics and to arithmetical functions
topic	Probabilités Random walks (statistiek) gtt Variables aléatoires Probabilities Random variables Zufallsvariable (DE-588)4129514-6 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd
topic_facet	Probabilités Random walks (statistiek) Variables aléatoires Probabilities Random variables Zufallsvariable Wahrscheinlichkeitsrechnung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013161873&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000001885
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Call Number:	0102 MAT 600f 2005 A 4535 Floor plan
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