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Asymptotic Normality Through Factorial Cumulants and Partition Identities

Published online by Cambridge University Press:  21 December 2012

KONSTANCJA BOBECKA ,
PAWEŁ HITCZENKO ,
FERNANDO LÓPEZ-BLÁZQUEZ ,
GRZEGORZ REMPAŁA  and
JACEK WESOŁOWSKI
KONSTANCJA BOBECKA
Affiliation:
Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa, Poland (e-mail: [email protected], [email protected])
PAWEŁ HITCZENKO
Affiliation:
Department of Mathematics, Drexel University, Philadelphia, USA (e-mail: [email protected])
FERNANDO LÓPEZ-BLÁZQUEZ
Affiliation:
Facultad de Matemáticas Universidad de Sevilla, Sevilla, Spain (e-mail: [email protected])
GRZEGORZ REMPAŁA
Affiliation:
Department of Biostatistics, Georgia Health University, Augusta, USA (e-mail: [email protected])
JACEK WESOŁOWSKI
Affiliation:
Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa, Poland (e-mail: [email protected], [email protected])
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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.

Keywords

Primary 60F05Secondary 60E10
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 2 , March 2013 , pp. 213 - 240
Copyright
Copyright © Cambridge University Press 2012

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