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Asymptotic normality through factorial cumulants and partition identities. (English) Zbl 1262.60023

Summary: 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 the negative multinomial distribution.

MSC:

60F05 Central limit and other weak theorems
60E10 Characteristic functions; other transforms
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