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- W2013082111 abstract "For r ⩾ 1, let M nr be the r th largest of {X 1 , …, X n }, where X 1 , X 2 ,… are i.i.d. random variables with common distribution function F such that F ( x ) < 1 for all x . Define μ ( x ) = F −1 (1 − x −1 ), x ⩾ 1. { M nr , n ⩾ r } is called regularly stable if M nr μ(n) → 1 in probability and (∗)μ(n 1 ) μ(n) → h(t) < ∞ for every t > 1. Several sets of necessary and sufficient conditions for regular stability are presented. In particular, { M nr } is regularly stable if and only if (∗) holds, and regular stability with h ( t ) ≡ 1 is tantamount to complete stability. Moreover, (∗) always implies the almost sure stability of { M nr }, r ⩾ 1." @default.
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- W2013082111 date "1999-01-01" @default.
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- W2013082111 title "Regular stability of large order statistics" @default.
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- W2013082111 doi "https://doi.org/10.1016/s0167-7152(98)00132-1" @default.
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