A characterization of probability distributions by mean values

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1 Scopus citations


Let Φ(X) be a measurable complex function on R;X, Y, Z be i.i.d. random variables; and φ{symbol}(t, u, v)=EΦ(tX+uY+nZ), where t, u, v∈R. In this paper we describe a class of function Φ(x) such that the distribution of X, Y, Z is determined by the funetion φ{symbol}(t, u, v). The main result is a generalization of the author's characterization of normal and stable distributions.

Original languageEnglish
Pages (from-to)691-700
Number of pages10
JournalJournal of Theoretical Probability
Issue number4
StatePublished - 1 Oct 1991
Externally publishedYes


  • Distribution
  • characterization
  • function
  • random variables

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty


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