%0 Generic %1 citeulike:1269836 %A Kossovsky, Alex E. %D 2007 %K digits leading phenomena %T Towards A Better Understanding Of The Leading Digits Phenomena %U http://arxiv.org/abs/math/0612627 %X This article on leading digits (Benford's Law) contains the following: (I) A comprehensive study of the leading digits phenomena, attempting to touch on all its existing explanations, proofs, and differing points of view. (II) The finding that leading digits of random numbers derived from a chain of distributions that are linked via parameter selection are logarithmic in the limit, and that empirically only around 3 or 4 sequences of such a distribution chain are needed to obtain results that are close enough to the logarithmic (i.e. rapid convergence). (III) An account on the existence of singularities in exponential growth rates with regards to the leading digits distributions of their series. (IV) A summary of a few special distributions that are intrinsically logarithmic. (V) A conceptual justification of Flehinger's iterated averaging scheme - an algorithm that was presented without any clear motivation. (VI) A note on the close relationship of Flehinger's scheme and the chain of distribution above to Hill's super distribution. (VII) A compelling argument justifying the scale invariance principle - a principle invoked in derivations of Benford's law. (VIII) A note on the intimate connection between one-sided tail to the right in density distributions and logarithmic leading digit behavior. (IX) An initial belief that there are fundamentally two and only two driving sources leading to the phenomena, one universal basis and another more specific cause, and that the two sources often overlap. (X) Some grand synthesis in relating these two sources and hence uniting all existing explanations.

@misc{citeulike:1269836, abstract = {This article on leading digits (Benford's Law) contains the following: (I) A comprehensive study of the leading digits phenomena, attempting to touch on all its existing explanations, proofs, and differing points of view. (II) The finding that leading digits of random numbers derived from a chain of distributions that are linked via parameter selection are logarithmic in the limit, and that empirically only around 3 or 4 sequences of such a distribution chain are needed to obtain results that are close enough to the logarithmic (i.e. rapid convergence). (III) An account on the existence of singularities in exponential growth rates with regards to the leading digits distributions of their series. (IV) A summary of a few special distributions that are intrinsically logarithmic. (V) A conceptual justification of Flehinger's iterated averaging scheme - an algorithm that was presented without any clear motivation. (VI) A note on the close relationship of Flehinger's scheme and the chain of distribution above to Hill's super distribution. (VII) A compelling argument justifying the scale invariance principle - a principle invoked in derivations of Benford's law. (VIII) A note on the intimate connection between one-sided tail to the right in density distributions and logarithmic leading digit behavior. (IX) An initial belief that there are fundamentally two and only two driving sources leading to the phenomena, one universal basis and another more specific cause, and that the two sources often overlap. (X) Some grand synthesis in relating these two sources and hence uniting all existing explanations.}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Kossovsky, Alex E.}, biburl = {https://www.bibsonomy.org/bibtex/2949ee79a36941a8316083e1536e21aac/a_olympia}, citeulike-article-id = {1269836}, description = {citeulike}, eprint = {math/0612627}, interhash = {811619559d2e3e5583b4176e0f709e6c}, intrahash = {949ee79a36941a8316083e1536e21aac}, keywords = {digits leading phenomena}, month = Apr, priority = {2}, timestamp = {2007-08-18T13:22:27.000+0200}, title = {Towards A Better Understanding Of The Leading Digits Phenomena}, url = {http://arxiv.org/abs/math/0612627}, year = 2007 }