In this paper, we will propose a way to accurately model certain naturally occurring collections of data. Through this proposed model, the proportion of d as leading digit, \(d\in \llbracket 1,9\rrbracket \), in data is more likely to follow a law whose probability distribution is determined by a specific upper bound, rather than Benford’s Law, as one might have expected. These probability distributions fluctuate nevertheless around Benford’s values. These peculiar fluctuations have often been observed in the literature in such data sets (where the physical, biological or economical quantities considered are upper bounded). Knowing beforehand the value of this upper bound enables to find, through the developed model, a better adjusted law than Benford’s one.

中文翻译：

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Benford与否Benford：在实验领域对优雅法则的系统性但并非总是有充分根据的使用

在本文中，我们将提出一种对某些自然发生的数据集合进行准确建模的方法。通过此提议的模型，d作为数据中前导数字\（d \ in \ llbracket 1,9 \ rrbracket \）的比例更可能遵循定律分布，该定律的概率分布由特定的上限确定，而不是正如人们所期望的那样，本福德定律。但是，这些概率分布围绕Benford的值波动。这些奇特的波动经常在此类数据集中的文献中被观察到（其中考虑的物理，生物学或经济量为上限）。事先了解这个上限的值，可以通过开发的模型找到比本福德定律更好的调整定律。