具有正则变化函数型随机足标的独立同分布序列最大值的极限分布
On the Limit Distribution of the Maximum of i. i. d.Sequence with Random Index as a Regularly Varying Function
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摘要: 设X1,X2,…为独立同分布序列(i.i.d.s.),Mn=max1≤i≤n Xi,实可测函数f(t)∈RVγ,γ>0,又设{N(n)}为一列取正整数的随机变量,满足N(n)/n p→η>0,得出了M[f(N(n))]的极限分布.Abstract: Let X1, X2, … be an i. i. d. sequence, and Mn = max1≤i≤n Xi, real measurable function f(t) ∈ RVγ,γ> 0. Suppose { N(n) } is a non-negative integer valued random variable with N(n)/n p→η> 0 as n→∞, the limit distribution of M[f(N(n))] is derived.
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