A characterization of multivariate \(l_ 1\)-norm symmetric distributions (Q1117637)
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scientific article; zbMATH DE number 4092578
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of multivariate \(l_ 1\)-norm symmetric distributions |
scientific article; zbMATH DE number 4092578 |
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A characterization of multivariate \(l_ 1\)-norm symmetric distributions (English)
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1989
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Let z be an \(n\times 1\) interchangeable random vector and \(z_{(1)}\leq...\leq z_{(n)}\) be its order statistics. Let \[ u_ i=(n- i+1)(z_{(i)}-z_{(i-1)}),\quad i=1,...,n,\quad with\quad z_{(0)}=0 \] and \(u=(u_ 1,...,u_ n)'\). The main result is that \(z=^{d}u\) iff z is a multivariate \(\ell_ 1\)-norm symmetric distribution.
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multivariate \(\ell 1\)-norm symmetric distribution
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normalized spacing
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survival function
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interchangeable random vector
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order statistics
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