Benfordness of Chains of Truncated Beta Distributions via a Piecewise Constant Approximation
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A chain of truncated distributions is constructed from iteratively truncating an initial distribution on the right. We show that if the initial distribution is a piecewise constant approximation of the Beta distribution with parameters \(\alpha \) and 1 then the mantissas of the chain of truncated distributions converge to a mantissa-limit distribution distinct from the Benford’s law. For general approximating initial distributions, under some suitable conditions on these mantissas, we can conclude that the mantissa-limit distributions converge to the mantissa-limit distribution for the limiting initial distribution. As a result, we obtain an alternative proof of the fact that chains of truncated Beta distributions satisfy Benford’s law in the limit.
KeywordsBenford’s law First significant digits Truncated distributions Beta distribution
The authors are grateful to the referees for their careful reading of the manuscript and their useful comments. The last author would like to thank the Development and Promotion of Science and Technology Talents Project (the DPST Scholarship) for the financial support.
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