Structure of Stieltjes classes of moment-equivalent probability laws

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:326

Article

Pakes, Anthony G.

关键词: indeterminate distributions;    Stieltjes class;    lognormal distribution;    infinite divisibility;   

DOI  :  10.1016/j.jmaa.2006.03.035

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free