Analiza wskazań wybranych mierników służących ocenie zgodności danych z prawem Benforda − przypadek pierwszej cyfry znaczącej
Analysis of indications for selected measures used in assessing data conformity to Benfordʼs law − the first significant digit case

Summary/Abstract: Comparing empirical distributions of the first significant digit, which are determined on the basis of the analysed data sets, to Benfordʼs distribution, often leads to the creation of rankings of the data sets. In order to do this, various measures of distributions similarity are employed, which allow to assess the level of similarity of the first non-zero significant digit empirical distribution to the aforementioned theoretical one. The paper presents the results of indications for thirteen measures of distributions similarity, using simulation data. In the study, the correlation analysis was employed. Moreover, an attempt to classify the measures of distributions similarity was made by means of the 𝒌-means method. The outcomes of clustering led to the conclusion that in the empirical research (aimed at the creation of analysed data sets rankings in terms of their level of similarity to Benfordʼs distribution), when one analyses data sets of different sizes, it is enough to use only four measures of this kind.

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