Abstract
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 language | English |
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Pages (from-to) | 1662-1665 |
Number of pages | 4 |
Journal | Statistics and Probability Letters |
Volume | 77 |
Issue number | 17 |
DOIs | |
Publication status | Published - Nov 1 2007 |
Keywords
- Data transformation
- Random walk
- Rayleigh model
- Self-normalized product
- Stable law
- Symmetric distribution
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty