Abstract

Various record achievements are recorded in a number of areas of human activity. In this case, some discretization of the obtained observation results repeatedly occurs with varying accuracy (up to a second, up to a meter, and up to a thousand individuals). Using exponential and geometric distributions as an example, we show how such a transition from continuous to discrete probability distributions changes the number of record values in the corresponding sequences of random variables.

中文翻译：

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关于将指数和几何记录随机变量联系起来的一些关系

摘要

在人类活动的许多领域中都记录了各种创纪录的成就。在这种情况下，所获得的观察结果的离散化会以不同的准确性（最多一秒，最多一米和最多一千个个体）反复发生。以指数和几何分布为例，我们说明了从连续概率分布到离散概率分布的这种转变如何改变相应随机变量序列中记录值的数量。