Scaling of the minimum of iid random variables

T. Y. Al-Naffouri*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Several areas in signal processing and communications rely on various tools in order statistics. Studying the scaling of the extreme values of iid random variables is of particular interest as it is sometimes only possible to make meaningful statements in the large number of variables case. This paper develops a new approach to finding the scaling of the minimum of iid variables by studying the behavior of the CDF and its derivatives at one point, or equivalently by studying the behavior of the characteristic function. The theory developed is used to study the scaling of several types of random variables and is confirmed by simulations.

Original languageEnglish (US)
Pages (from-to)1830-1834
Number of pages5
JournalSignal Processing
Issue number9
StatePublished - Sep 2009


  • Characteristic function
  • Extreme values
  • Initial value theorem
  • Order statistics
  • Scaling of random variables

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Vision and Pattern Recognition


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