Limit distributions for compounded sums of extreme order statistics
Keyword(s):
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.
1992 ◽
Vol 29
(03)
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pp. 557-574
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1978 ◽
Vol 21
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pp. 447-459
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2003 ◽
Vol 40
(01)
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pp. 226-241
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1965 ◽
Vol 116
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pp. 474-474
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1978 ◽
Vol 15
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pp. 639-644
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Keyword(s):
1999 ◽
Vol 36
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pp. 194-210
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