Limit distributions for compounded sums of extreme order statistics
- 1 September 1992
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 29 (3) , 557-574
- https://doi.org/10.2307/3214893
Abstract
LetX(1)≦X(2)≦ ·· ·≦X(N(t))be the order statistics of the firstN(t) elements from a sequence of independent identically distributed random variables, where {N(t);t≧ 0} is a renewal counting process independent of the sequence ofX's. We give a complete description of the asymptotic distribution of sums made from the topktextreme values, for any sequencektsuch thatkt→ ∞,kt/t→ 0 ast→ ∞. We discuss applications to reinsurance policies based on large claims.Keywords
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