可数字母表上的吸引域

摘要：

对于可数字母表上的每个概率分布，基于图灵的观点，开发了一系列正泛函作为尾部指标。通过且仅通过这些指数的渐近行为，定义了字母表上所有概率分布的吸引域。的三个主要领域的吸引力分别包含厚尾，薄尾和没有尾巴的分布，类似于平行的三个主要领域的吸引力，Gumbel，Frechet和Weibull家族，为连续随机变量在实数线上。除了与域相关的概率优点之外，尾部指数部分地受到以下事实的激励：对于序列中的每个指数存在无偏估计，因此，只要样本足够大，就可以在统计上观察到。

英文摘要：

For each probability distribution on a countable alphabet, a sequence of positive functionals are developed as tail indices based on Turing's perspective. By and only by the asymptotic behavior of these indices, domains of attraction for all probability distributions on the alphabet are defined. The three main domains of attraction are shown to contain distributions with thick tails, thin tails and no tails respectively, resembling in parallel the three main domains of attraction, Gumbel, Frechet and Weibull families, for continuous random variables on the real line. In addition to the probabilistic merits associated with the domains, the tail indices are partially motivated by the fact that there exists an unbiased estimator for every index in the sequence, which is therefore statistically observable, provided that the sample is sufficiently large.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。