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<p>In Rényi’s representation for exponential order statistics, we replace the iid exponential sequence with any iid sequence, and call the resulting order statistic <i>generalized Rényi statistic</i>. We prove that by randomly reordering the variables in the generalized Rényi statistic, we obtain in the limit a sequence of iid exponentials. This result allows us to propose a new model for heavy-tailed data. Although the new model is very close to the classical iid framework, we establish that the Hill estimator is weakly consistent and asymptotically normal without any further assumptions on the underlying distribution or on the number of upper order statistics used in the estimator.</p>

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Generalized Rényi statistics

  • 期刊论文

  • 发表日期：

    2025年3月31日

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  • Péter Kevei,
  • László Viharos

摘要

In Rényi’s representation for exponential order statistics, we replace the iid exponential sequence with any iid sequence, and call the resulting order statistic generalized Rényi statistic. We prove that by randomly reordering the variables in the generalized Rényi statistic, we obtain in the limit a sequence of iid exponentials. This result allows us to propose a new model for heavy-tailed data. Although the new model is very close to the classical iid framework, we establish that the Hill estimator is weakly consistent and asymptotically normal without any further assumptions on the underlying distribution or on the number of upper order statistics used in the estimator.