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In many real life situations, it is observed that the first digits (i.e.,$1,2,\ldots,9$) of a numerical data-set, which is expressed using decimalsystem, do not follow a random distribution. Instead, smaller numbers arefavoured by nature in accordance with a logarithmic distribution law, which isreferred to as Benford's law. The existence and applicability of this empiricallaw have been extensively studied by physicists, accountants, computerscientists, mathematicians, statisticians, etc., and it has been observed thata large number of data-sets related to diverse problems follow thisdistribution. However, applicability of Benford's law has been hardly testedfor extrasolar objects. Motivated by this fact, this paper investigates theexistence of Benford's distribution in the extrasolar world using Kepler datafor exoplanets. The investigation has revealed the presence of Benford'sdistribution in various physical properties of these exoplanets. Further,Benford goodness parameters are computed to provide a quantitative measure ofcoincidence of real data with the ideal values obtained from Benford'sdistribution. The quantitative analysis and the plots have revealed thatseveral physical parameters associated with the exoplanets (e.g., mass, volume,density, orbital semi-major axis, orbital period, and radial velocity) nicelyfollow Benford's distribution, whereas some physical parameters (e.g., totalproper motion, stellar age and stellar distance) moderately follow thedistribution, and some others (e.g., longitude, radius, and effectivetemperature) do not follow Benford's distribution. Further, some specificcomments have been made on the possible generalizations of the obtained result,its potential applications in analyzing data-set of candidate exoplanets, andhow interested readers can perform similar investigations on other interestingdata-sets.

Benford's distribution in extrasolar world: Do the exoplanets follow Benford's distribution?