Journal article
Asymptotic Normality Through Factorial Cumulants and Partition Identities
Combinatorics, probability & computing, v 22(2), pp 213-240
Mar 2013
PMID: 24591773
Abstract
In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for ‘moments’ of partitions of numbers. The general limiting result is then used to (re-)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution.
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Details
- Title
- Asymptotic Normality Through Factorial Cumulants and Partition Identities
- Creators
- KONSTANCJA BOBECKA - 1Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa, Poland (e-mail: bobecka@mini.pw.edu.pl, wesolo@mini.pw.edu.pl)PAWEŁ HITCZENKO - 2Department of Mathematics, Drexel University, Philadelphia, USA (e-mail: phitczenko@math.drexel.edu)FERNANDO LÓPEZ-BLÁZQUEZ - 3Facultad de Matemáticas Universidad de Sevilla, Sevilla, Spain (e-mail: lopez@us.es)GRZEGORZ REMPAŁA - 4Department of Biostatistics, Georgia Health University, Augusta, USA (e-mail: grempala@georgiahealth.edu)JACEK WESOŁOWSKI - 1Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa, Poland (e-mail: bobecka@mini.pw.edu.pl, wesolo@mini.pw.edu.pl)
- Publication Details
- Combinatorics, probability & computing, v 22(2), pp 213-240
- Publisher
- Cambridge University Press; Cambridge, UK
- Number of pages
- 28
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000314296400003
- Scopus ID
- 2-s2.0-84873361507
- Other Identifier
- 991014878504804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Computer Science, Theory & Methods
- Mathematics
- Statistics & Probability