Properties of Extreme Order Statistics and Their Application to Fire Losses and Earthquake Magnitudes

1981 ◽  
pp. 351-366 ◽  
Author(s):  
G. Ramachandran
Keyword(s):  
Order Statistics ◽  
Extreme Order Statistics

Limit distributions for compounded sums of extreme order statistics

1992 ◽  
Vol 29 (03) ◽  
pp. 557-574 ◽  
Author(s):  
Jan Beirlant ◽  
Jozef L. Teugels
Keyword(s):  
Order Statistics ◽  
Asymptotic Distribution ◽  
Counting Process ◽  
Extreme Values ◽  
Random Variables ◽  
Limit Distributions ◽  
Extreme Order Statistics ◽  
Renewal Counting Process ◽  
Independent Identically Distributed

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.

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