A Statistical Derivation of the Significant-Digit Law

By T. Hill. 1995

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In Statistics and Probability

Citations in the corpus

Not the First Digit! Using Benford's Law to Detect Fraudulent Scientif ic Data (2007, methodology): “Newcomb also derived the formulas for the first and second significant digit (Hill, 1995a , p.”
Detecting Fraud in Data Sets Using Benford's Law (2004, background): “Hill (1995) extends this to the general law given by P D1 · · ·Dk = d1 · · ·dk = log10 1+ d1 dk −1 Hence, the probability of getting a number with the first two significant digits of 32 is P D1D2 = 32 = log10 1+ 32 −1 = 01336.”
The New C Standard (Excerpted material) An Economic and Cultural Commentary (2008, unknown): “, Benford’s law).[3] While the results for decimal-constant (see Figure 825.”
The effective use of Benford's Law to assist in detecting fraud in accounting data (2004, methodology): “Diaconis and Freedman (1979) offer convincing evidence that Benford manipulated round-off errors to obtain a better fit to a logarithmic law, but even the non-manipulated data are a remarkably good fit (Hill 1995).”
One-dimensional dynamical systems and Benford's law (2004, background): “Since Benford’s article, numerous examples of empirical data sets following Benford’s law have been found in real-life data (e.g., physical constants, stock market indices, tax returns [ H2 , R]); in stochastic processes (e.g., sums and products of random variables [R, S]); and in many deterministic”
Mathematical and Statistical Methods for Actuarial Sciences and Finance (2014, methodology): “7 This window period is suggested in [6].”
Breaking the (Benford) Law (2007, background): “About a century after Newcomb’s discovery, rigorous proof of the law (and derivation of when and why it holds) were finally developed (Hill 1995).”
Statistical fraud detection: A review (2002, background): “Benford's law (Hill, 1995) says that the distribution of the first significant digits of numbers drawn from a wide variety of random distributions will have (asymptotically) a certain form.”
A generalized Benford's law for JPEG coefficients and its applications in image forensics (2007, background): “Benford’s law [3-5], also known as the first digit law or significant digit law, is an empirical law.”
A Simple Explanation of Benford's Law (2009, background): “It is commonly accepted that the first rigorous explanation of the law was due to Hill (1995), who provided a measure-theoretical proof that data drawn from a random mix of different distributions—rather like Frank Benford’s original 20,000—will ultimately converge to Benford’s law.”
The Quality of China's GDP Statistics (2014, unknown): “The Benford distribution is the only distribution with these properties (Pinkham, 1961, Hill, 1995a/b and 1998).79 To use Benford’s Law to check for data falsification requires the assumption that the true data follow the Benford distribution.”
Fact and Fiction in EU-Governmental Economic Data (2011, background): “Published by Blackwell Published Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. distributions (cf. Hill, 1995b, pp. 888–889).”