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Remark on rates of convergence to extreme value distributions via the Stein equations

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Consider the maximum of independent and identically distributed random variables. The classical result says that the renormalized sample maximum converges to an extreme value distributions, under certain conditions on the… Click to show full abstract

Consider the maximum of independent and identically distributed random variables. The classical result says that the renormalized sample maximum converges to an extreme value distributions, under certain conditions on the distribution function. In the present paper, we shall study the uniform rate of the convergence with respect to the Kolmogorov distance in the framework of the Stein equations. Some typical examples are raised in the paper.

Keywords: remark rates; extreme value; value distributions; rates convergence; stein equations

Journal Title: Extremes
Year Published: 2020

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