An unusual strong law of large numbers for the largest observation of a triangular array (Q2756179)
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scientific article; zbMATH DE number 1672634
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An unusual strong law of large numbers for the largest observation of a triangular array |
scientific article; zbMATH DE number 1672634 |
Statements
29 July 2002
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almost sure convergence
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order statistics
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strong law of large numbers
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0.93053174
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0.9255215
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0.90976125
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0.9065729
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An unusual strong law of large numbers for the largest observation of a triangular array (English)
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For a triangular array \(\{X, X_{nj}, 1\leq j\leq n, n\geq 1\}\) of independent identically distributed random variables with common density \(f(x)= px^{-p-1}I\{x\geq 1\}\), \(p>0\) and \(pk= 1\), the strong law of large numbers of the \(k\)th order statistic is proved. In particular, if \(p= 1=k\), the strong law for the largest observation is valid.
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