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Regazzini, E (1982)

La legge di Benford-Furlan come legge statistica (The Benford-Furlan law as a statistical law)

Statistica 42(3), 351-370.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.



Abstract: SUMMARY: The well-known Benford-Furlan law in the first digit problem is seen as a `probable' or `statistical' law. This point of view, when we are faced with the problem of predicting the first digit of unobserved statistical data, involves the assessment of the probability distribution of an infinite sequence of random quantities (r.q.) with values in {1, ... ,9}. If the condition of exchangeability of these r.q.'s X1, X2, ... is assumed, then, by a theorem due to B. de Finetti, there exists a random vector ϴ, with values in [0,1]9, such that P(X1=x1, ..., Xn=xn|ϴ=θ)=θx1 ... θxn, xi∈{1, ..., 9}, (i=1, ...,n); ∑19θ_j=1, θj≥0 (j=1, ...,9); n=1,2, ... . The vector ϴ is the limit, in the sense of strong convergence, of the sequence of the random vectors of the relative frequencies of 1, ...,9 in the sample. We study the Benford-Furlan law as an element of the space of the distribution functions which are the limits of the frequencies mentioned above. The probability law on this space, according to the Bayes theorem, changes on the basis of the empirical observations. We give some conditions which characterize the Benford-Furlan law as a probability function of Xn on {1, ... ,9}. We also justify the Dirichlet distribution as a probability law of ϴ beginning from the consideration of a noninformative and finitely additive prior distribution characterized via a natural property of the expectation of the predictive distribution


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Reference Type: Journal Article

Subject Area(s): Statistics