Limit distributions for compounded sums of extreme order statistics
1992 ◽
Vol 29
(03)
◽
pp. 557-574
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Keyword(s):
Let X (1) ≦ X (2) ≦ ·· ·≦ X (N(t)) be the order statistics of the first N(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 of X's. We give a complete description of the asymptotic distribution of sums made from the top kt extreme values, for any sequence kt such that kt → ∞, kt /t → 0 as t → ∞. We discuss applications to reinsurance policies based on large claims.
1978 ◽
Vol 21
(4)
◽
pp. 447-459
◽
2003 ◽
Vol 40
(01)
◽
pp. 226-241
◽
1965 ◽
Vol 116
◽
pp. 474-474
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1978 ◽
Vol 15
(03)
◽
pp. 639-644
◽
Keyword(s):
1999 ◽
Vol 36
(01)
◽
pp. 194-210
◽