Structure of Stieltjes classes of moment-equivalent probability laws

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23 Citations (Scopus)


A Stieltjes class is a one-parameter family of moment-equivalent distribution functions constructed by modulation of a given indeterminate distribution function F, called the center of the class. Members of a Stieltjes class are mutually absolutely continuous, and conversely, any pair of moment-equivalent and mutually absolutely continuous distribution functions can be joined by a Stieltjes class. The center of a Stieltjes class is an equally weighted mixture of its extreme members, and this places restrictions on which distributions can belong to a Stieltjes class with a given center. The lognormal law provides interesting illustrations of the general ideas. In particular, it is possible for two moment equivalent infinitely divisible distributions to be joined by a Stieltjes class, and random scaling can be used to construct new Stieltjes classes from a given Stieltjes class. (c) 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)1268-1290
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 2007


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