2017 / December Volume 12 No.4
Strong laws for the largest ratio of adjacent order statistics
| Published Date |
2017 / December
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|---|---|
| Title | Strong laws for the largest ratio of adjacent order statistics |
| Author | |
| Keyword | |
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| Pagination | 315-323 |
| Abstract | Consider independent and identically distributed random variables
$\{X_{n,k}$, $1\le k\le m_n, n \ge 1\}$. We order this data set, $X_{n(1)}< X_{n(2)}< X_{n(3)}< \cdots < X_{n(m_n-1)}< X_{n(m_n)}$. Then we find the ratio of these adjacent order statistics. Our random variable of interest is the largest of these adjacent ratios, $\max_{2\le k \le m_n} X_{n(k)}/X_{n(k-1)}$. We obtain various limit theorems for this random variable. |
| DOI | |
| AMS Subject Classification |
60F15.
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| Received |
2017-06-18
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| Accepted |
2017-11-24
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