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We explain Kossovsky's generalization of Benford's law which is a formula
that approximates the distribution of leftmost digits in finite sequences of
natural data and apply it to six sequences of data including populations of US
cities and towns and times between earthquakes. We model the natural logarithms
of these two data sequences as samples of random variables having normal and
reflected Gumbel densities respectively. We show that compliance with the
general law depends on how nearly constant the periodized density functions are
and that the models are generally more compliant than the natural data. This
surprising result suggests that the generalized law might be used to improve
density estimation which is the basis of statistical pattern recognition,
machine learning and data science.

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