Lorenz ordering of order statistics (Q850194)
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scientific article; zbMATH DE number 5072672
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lorenz ordering of order statistics |
scientific article; zbMATH DE number 5072672 |
Statements
Lorenz ordering of order statistics (English)
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15 November 2006
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Let \(X_{i:n}\) denote the \(i\)th order statistic of a random sample of size \(n\) from a continuous distribution with cdf\,\(F\). Sufficient conditions are obtained on \(F\) so that \(X_{j:m}\leq_* X_{i:n}\) (hence \(X_{j:m}\leq_{\text{Lorenz}}X_{i:n})\) for \(i\leq j\) and \(n-i\geq m-j\).
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star ordering
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dispersive ordering
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Hazard rate
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reverse Hazard rate
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