A connection between self-normalized products and stable laws

Igor Melnykov, John T. Chen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let X1, ..., Xn constitute a random sample from a population with underpinning cumulative distribution function F (x). For any value 0 < α < 1, we prove that under a condition of stable laws, the self-normalized product n1 / 2 α X1 X2 ... Xn / sqrt(∑* Xi12 ... Xin - 12) follows the same distribution as X1, where ∑* denotes the sum of over all permissible sequences of integers 1 ≤ i1 < i2 < ⋯ < in - 1 ≤ n.

Original languageEnglish (US)
Pages (from-to)1662-1665
Number of pages4
JournalStatistics and Probability Letters
Issue number17
StatePublished - Nov 2007
Externally publishedYes


  • Data transformation
  • Random walk
  • Rayleigh model
  • Self-normalized product
  • Stable law
  • Symmetric distribution


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