Summary
LetX 1,X 2, ...,X n be a sequence of positive, independent, identically distributed random variables with the same distribution function (d.f.)F and denote byX 1:n ≦X 2:n ≦...≦X n:n the order statistics of the sample. We characterize the class of d.f.F for which
for fixedn andi (i≦n-1), and we show that it is independent ofn. This leads to the genesis of a new class of d.f.L i ; we show that the sequence (L i ) ∞ i =0 is strictly decreasing and we illustrate how the classesL i determine the probabilistic structure of the classL of subexponential distributions.
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Research Assistent of the Belgian National Fund for Scientific Research
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Willekens, E. The structure of the class of subexponential distributions. Probab. Th. Rel. Fields 77, 567–581 (1988). https://doi.org/10.1007/BF00959618
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DOI: https://doi.org/10.1007/BF00959618
Keywords
- Distribution Function
- Stochastic Process
- Probability Theory
- Order Statistic
- Mathematical Biology