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引用次数: 1
摘要
De Haan和Resnick[Ann.Probab.10（1982），no.2396–413]已经表明，具有连续可微密度的独立同分布（iid）随机变量的归一化样本极大值的β\β阶Rényi熵（β>1\β>1）收敛于极大稳定律的β\贝塔阶Rény熵。本文讨论了极值理论中密度函数的收敛速度。最后，我们研究了Rényi熵在归一化样本最大值情况下的收敛速度。
A comment on rates of convergence for density function in extreme value theory and Rényi entropy
De Haan and Resnick [Ann. Probab. 10 (1982), no. 2, 396–413] have shown that the Rényi entropy of order
β
\beta
(
β
>
1
\beta >1
) of normalized sample maximum of independent and identically distributed (iid) random variables with continuous differentiable density converges to the Rényi entropy of order
β
\beta
of a max stable law. In this paper, we review the rate of convergence for density function in extreme value theory. Finally, we study the rate of convergence for Rényi entropy in the case of normalized sample maxima.
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