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Poisson approximation:

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Bibliographic Details
Main Authors:	Barbour, Andrew D. 1947- (Author), Holst, Lars (Author), Janson, Svante 1955- (Author)
Format:	Book
Language:	English
Published:	Oxford Clarendon Press 1992
Series:	Oxford studies in probability 2
Subjects:	Poisson-Verteilung Poisson-Prozess Approximationstheorie Stochastischer Prozess
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003474461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	X, 277 S.
ISBN:	0198522355

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Record in the Search Index

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adam_text	Contents 1. Introduction 1 2. Upper bounds 21 2.1 Upper bounds and monotonicity 24 2.2 Existence of monotone couplings 27 Associated random variables 29 Negatively associated random variables 30 Gaussian random variables 32 2.3 Independent and dissociated summands 33 2.4 Miscellany 41 3. Lower bounds 49 3.1 General lower bounds 49 3.2 Lower bounds under monotonicity 58 3.3 Lower bounds for mixed Poisson approximation 68 3.4 Illustrative examples 69 4. Random permutations 76 4.1 A general result 77 4.2 Matching problems 80 4.3 The menage problem 83 4.4 Higher order arrays 85 5. Random graphs 89 5.1 Subgraphs in Kn p 89 5.2 Vertex degrees 97 5.3 Coloured graphs and birthday problems 104 5.4 Complete graphs with repulsions 109 6. Occupancy and urn models 112 6.1 Drawing without replacement 112 6.2 Multinomial allocations 114 Left hand domain 114 Right hand domain 122 Exact box counts 125 6.3 Urn models and general occupancy 129 6.4 A matrix occupancy problem 130 7. Spacings 134 7.1 Couplings 134 7.2 Ordinary spacings 136 7.3 m Spacings 138 7.4 Higher dimensions 144 7.5 An application to DNA breakage 148 x Poisson approximation 8. Exceedances and extremes 150 8.1 The Gaussian case 150 8.2 The scan statistic for Poisson processes 156 8.3 Extremes of associated random variables 160 8.4 Patterns and runs 162 8.5 Rare sets in Markov chains 165 9. Independent and dissociated terms 170 9.1 Independent summands 171 9.2 Binomial approximation 188 9.3 Dissociated summands 193 10. Poisson process approximation 202 10.1 The basic method 205 10.2 Improved rates 217 10.3 Multivariate Poisson approximation 235 10.4 Compound Poisson approximation 238 10.5 Further developments 244 Appendix 253 A.I Probability metrics 253 Total variation distance 253 Wasserstein distance 254 Hellinger distance 255 A.2 Poisson and binomial estimates 257 References 264 Index 273
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isbn	0198522355
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publishDate	1992
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series	Oxford studies in probability
series2	Oxford studies in probability
spellingShingle	Barbour, Andrew D. 1947- Holst, Lars Janson, Svante 1955- Poisson approximation Oxford studies in probability Poisson-Verteilung (DE-588)4253010-6 gnd Poisson-Prozess (DE-588)4174971-6 gnd Approximationstheorie (DE-588)4120913-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd
subject_GND	(DE-588)4253010-6 (DE-588)4174971-6 (DE-588)4120913-8 (DE-588)4057630-9
title	Poisson approximation
title_auth	Poisson approximation
title_exact_search	Poisson approximation
title_full	Poisson approximation A. D. Barbour ; Lars Holst ; Svante Janson
title_fullStr	Poisson approximation A. D. Barbour ; Lars Holst ; Svante Janson
title_full_unstemmed	Poisson approximation A. D. Barbour ; Lars Holst ; Svante Janson
title_short	Poisson approximation
title_sort	poisson approximation
topic	Poisson-Verteilung (DE-588)4253010-6 gnd Poisson-Prozess (DE-588)4174971-6 gnd Approximationstheorie (DE-588)4120913-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd
topic_facet	Poisson-Verteilung Poisson-Prozess Approximationstheorie Stochastischer Prozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003474461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV005125282
work_keys_str_mv	AT barbourandrewd poissonapproximation AT holstlars poissonapproximation AT jansonsvante poissonapproximation

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