Asymptotic normality through factorial cumulants and partitions identities

Konstancja Bobecka; Pawel Hitczenko; Fernando Lopez-Blazquez; Grzegorz Rempala; Jacek Wesolowski

doi:10.1017/so963548312000545

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arXiv · 1106.4684

Asymptotic normality through factorial cumulants and partitions identities

Konstancja Bobecka·Pawel Hitczenko·Fernando Lopez-Blazquez·Grzegorz Rempala·Jacek Wesolowski

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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.

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Konstancja Bobecka, Pawel Hitczenko, Fernando Lopez-Blazquez, Grzegorz Rempala, Jacek Wesolowski. 2013-01-01. Asymptotic normality through factorial cumulants and partitions identities. https://doi.org/10.1017/so963548312000545

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