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 < i2 < ⋯ < in - 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 < i2 < ⋯ < in - 1 ≤ n.
KW - Data transformation
KW - Random walk
KW - Rayleigh model
KW - Self-normalized product
KW - Stable law
KW - Symmetric distribution
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U2 - 10.1016/j.spl.2007.04.023
DO - 10.1016/j.spl.2007.04.023
M3 - Article
AN - SCOPUS:35348826100
SN - 0167-7152
VL - 77
SP - 1662
EP - 1665
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 17
ER -