Linearity of convex mean residual life (Q5955595)
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scientific article; zbMATH DE number 1705585
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linearity of convex mean residual life |
scientific article; zbMATH DE number 1705585 |
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Linearity of convex mean residual life (English)
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7 March 2002
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characterization
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conditional expectation
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For a random variable \(X\) with distribution function \(F(x)\) define NEWLINE\[NEWLINEM(a,z)= aE(X\mid X\leq z)+(1-a) E(X\mid X>z),NEWLINE\]NEWLINE where \(0\leq a\leq 1\), and \(z\) is such that \(0<F(z)<1\). The authors show that the linearity of \(M(a,z)\) characterizes \(F(z)\) upto a scale parameter. Closed forms of \(F(z)\) are given only for three values of \(A\), assuming that \(M(1/2,z)=Az\).
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