Benford’s Law is a statistical regularity of a large number of datasets; assessing the compliance of a large dataset with the Benford’s Law is a theme of remarkable relevance, mainly for its practical consequences. Such a task can be faced by introducing a statistical distance concept between the empirical distribution of the data and the random variable associated with Benford’s Law. This paper deals with the problem of measuring the compliance of a random variable –which can be seen as describing the empirical distri- bution of a collection of data –with the Benford’s Law. It proposes a statistical methodology for detecting the critical values related to conformity/nonconformity with Benford’s Law in some well-established cases of statistical distance. The followed approach is grounded on the proper selection of a family of paramet- ric random variables –the lognormal distribution, in our case –and of a reference statistical distance concept –mean absolute deviation. A discussion of the obtained results is carried out on the ground of the existing literature. Moreover, some open problems are also presented.
Data validity and statistical conformity with Benford's Law / Cerqueti, R; Maggi, M. - In: CHAOS, SOLITONS & FRACTALS. - ISSN 1873-2887. - 144:(2021), pp. 1-7.
Data validity and statistical conformity with Benford's Law
Cerqueti, R;
2021
Abstract
Benford’s Law is a statistical regularity of a large number of datasets; assessing the compliance of a large dataset with the Benford’s Law is a theme of remarkable relevance, mainly for its practical consequences. Such a task can be faced by introducing a statistical distance concept between the empirical distribution of the data and the random variable associated with Benford’s Law. This paper deals with the problem of measuring the compliance of a random variable –which can be seen as describing the empirical distri- bution of a collection of data –with the Benford’s Law. It proposes a statistical methodology for detecting the critical values related to conformity/nonconformity with Benford’s Law in some well-established cases of statistical distance. The followed approach is grounded on the proper selection of a family of paramet- ric random variables –the lognormal distribution, in our case –and of a reference statistical distance concept –mean absolute deviation. A discussion of the obtained results is carried out on the ground of the existing literature. Moreover, some open problems are also presented.File | Dimensione | Formato | |
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