Uniform approximation of the tail probability of weighted sums of subexponential random variables

Chenhua Zhang and Shaobai Kan

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 21, 6290-6298

Abstract: For subexponential random variables Xi, 1 ⩽ i ⩽ n, the uniform asymptotic result P∑i=1nciXi+>x∼P∑i=1nciXi>x∼∑i=1nP(ciXi>x) \begin{eqnarray*} P\bigg (\sum _{i=1}^n c_i X_i^+>x\bigg ) \sim P\bigg (\sum _{i=1}^n c_iX_i>x\bigg ) \sim \sum _{i=1}^n P(c_iX_i>x) \end{eqnarray*} is established for 0

Date: 2016
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DOI: 10.1080/03610926.2014.960585

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