Random contraction and random dilation of generalized order statistics

Eric Beutner, Udo Kamps*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Distributional equations of the form [image omitted] are studied, where X and Y are neighboring generalized order statistics based on distribution function F, and V is a power function or Pareto distributed random variable, independent of Y. Characterizations of distributions via random contraction and random dilation are stated involving three conditions, namely, the distributional equation, the form of F and the distribution of V, where each two assertions imply the third. Recent results for the particular submodels of order statistics and record values are contained and also extended.

Original languageEnglish
Pages (from-to)2185-2201
Number of pages17
JournalCommunications in Statistics - Theory and Methods
Issue number14
Publication statusPublished - 1 Jan 2008
Externally publishedYes


  • Characterizations of distributions
  • Distributional equation
  • Generalized order statistics
  • Mellin transform
  • Pareto distribution
  • Power function distribution
  • Weibull distribution


Dive into the research topics of 'Random contraction and random dilation of generalized order statistics'. Together they form a unique fingerprint.

Cite this