Characterizations of shift-invariant distributions based on summation modulo one

R.J.G. Wilms, J.G.F. Thiemann

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Let X1Y1,…, Yn be independent random variables. We characterize the distributions of X and Yj satisfying the equation {X+Y1++Yn}=dX, where {Z} denotes the fractional part of a random variable Z. In the case of full generality, either X is uniformly distributed on [0,1), or Yj has.a shifted lattice distribution and X is shift‐invariant. We also give a characterization of shift‐invariant distributions. Finally, we consider some special cases of this equation.
Original languageEnglish
Pages (from-to)351-354
JournalAustralian Journal of Statistics
Volume36
Issue number3
DOIs
Publication statusPublished - 1994

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