2005 / March Volume 32 No.1
Exact laws for randomly selected order statistics
| Published Date |
2005 / March
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|---|---|
| Title | Exact laws for randomly selected order statistics |
| Author | |
| Keyword | |
| Download | |
| Pagination | 1-19 |
| Abstract | Let $\{ X, X_{nj} , 1 \le j \le m, n \ge 1 \}$ be i.i.d. random variables with a generalized Pareto distribution where $EX = \infty$. We randomly select one of our order statistics
from $\{ X_{n(1)} , \ldots , X_{n(m)} \}$ with a predetermined set of probabilities. Calling that new random variable $Y_n$ we explore whether or not we can obtain constants an and $b_N$ so that $\sum_{n=1}^N a_nY_n / b_n$ converges in some sense to a nonzero constant, thus creating an
Exact Law of Large Numbers.
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| AMS Subject Classification |
60F15, 60F05
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| Received |
2003-11-27
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