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 |
|---|---|
| Pages (from-to) | 1662-1665 |
| Number of pages | 4 |
| Journal | Statistics and Probability Letters |
| Volume | 77 |
| Issue number | 17 |
| DOIs | |
| Publication status | Published - Nov 2007 |
| Externally published | Yes |
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Keywords
- Data transformation
- Random walk
- Rayleigh model
- Self-normalized product
- Stable law
- Symmetric distribution
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Statistics and Probability
Cite this
A connection between self-normalized products and stable laws. / Melnykov, Igor; Chen, John T.
In: Statistics and Probability Letters, Vol. 77, No. 17, 11.2007, p. 1662-1665.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A connection between self-normalized products and stable laws
AU - Melnykov, Igor
AU - Chen, John T.
PY - 2007/11
Y1 - 2007/11
N2 - 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 2 <⋯ n - 1 ≤ n.
AB - 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 2 <⋯ n - 1 ≤ n.
KW - Data transformation
KW - Random walk
KW - Rayleigh model
KW - Self-normalized product
KW - Stable law
KW - Symmetric distribution
UR - http://www.scopus.com/inward/record.url?scp=35348826100&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=35348826100&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2007.04.023
DO - 10.1016/j.spl.2007.04.023
M3 - Article
VL - 77
SP - 1662
EP - 1665
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
IS - 17
ER -