| Adhikari, AK (1969). Some Results on Distribution of Most Significant Digit. Sankhya-The Indian Journal of Statistics Series B, 31 (Dec), 413-420. ISSN:0581-5738. |
 |
|
|
|
| Adhikari, AK and Sarkar, BP (1968). Distributions of most significant digit in certain functions whose arguments are random variables. Sankhya-The Indian Journal of Statistics Series B, no. 30, 47-58. |
 |
|
|
|
| Altamirano, C and Robledo, A (2009). Generalized Thermodynamics underlying the laws of Zipf and Benford. pp 2232-2237 in: J. Zhou (ed.), Complex Sciences 2009, Part II, LNICST 5. ISSN:1867-8211. |
 |
|
|
|
| Arita, M (2005). Scale-freeness and biological networks. Journal of Biochemistry, 138 (1): 1-4. ISSN:0021-924X. |
 |
|
|
|
| Ashcraft, MH (1992). Cognitive arithmetic: A review of data and theory. Cognition 44 (Aug), 75-106. |
 |
|
|
|
| Ashcraft, MH and Christy, KS (1995). The Frequency of Arithmetic Facts in Elementary Texts: Addition and Multiplication in Grades 1-6. Journal for Research in Mathematics Education 26, 396-421. |
 |
|
|
|
| Auffhammer, M and Carson, RT (2006). Offsetting Reductions From Kyoto And Then Some: Forecasts of China’s CO2 Emissions Using Province Level Data. Draft 7 Sep 2006. |
 |
|
|
|
| Auffhammer, M and Carson, RT (2008). Forecasting the path of China's CO2 emissions using province-level information. J. Environ. Econ. Manage. 55(3), 229-247. ISSN:0095-0696. |
 |
|
|
|
| Baer, MB (2006). Rényi to Rényi - Source Coding under Siege. (accepted to ISIT 2006). |
 |
|
|
|
| Baer, MB (2006). Prefix coding under Siege. (submitted to IEEE Trans. Inform. Theory). |
 |
|
|
|
| Baer, MB (2007). Reserved-Length Prefix Coding. (submitted to ISIT 2008). |
 |
|
|
|
| Baer, MB (2007). Bounds on Generalized Huffman Codes. |
 |
|
|
|
| Bailly, N (2006). Prominence trend in maximum lengths recorded for fishes: a preliminary analysis. pp 12-17 in: Palomares, MLD, Stergiou, KI, and Pauly, D (eds.), Fishes in databases and ecosystems. Proceedings of the 2006 FishBase Symposium. Fisheries Centre Research Reports, 2006, Vol. 14, No. 4. ISSN:1198-6727. |
 |
|
|
|
| Banks, WP and Hill, DK (1974). The Apparent Magnitude of Number Scaled by Random Production. Journal of Experimental Psychology 102 (2), 353-376. ISSN:0022-1015. |
 |
|
|
|
| Barlow, JL and Bareiss, EH (1985). On Roundoff Error Distributions in Floating Point and Logarithmic Arithmetic. Computing 34(4), 325-347. ISSN:0010-485X. |
 |
|
|
|
| Barnard, PJ, Scott, SK and May, J (2001). When the central executive lets us down: Schemas, attention, and load in a generative working memory task. Memory, 9 (4-6), 209-221. ISSN:0965-8211. |
 |
|
|
|
| Becker, PW (1982). Patterns in Listings of Failure-Rate and MTTF Values and Listings of Other Data. IEEE Transactions on Reliability 31(2), 132-134. ISSN:0018-9529. |
 |
|
|
|
| Beeli, G, Esslen, M and Jäncke, L (2007). Frequency Correlates in Grapheme-Color Synaesthesia. Psychological Science, 18(9), 788-792. ISSN:0956-7976. |
 |
|
|
|
| Beer, TW (2009). Terminal digit preference: beware of Benford's law. Journal of Clinical Pathology 62(2), 192. |
 |
|
|
|
| Bensmail, H and Haoudi, A (2003). Postgenomics: Proteomics and Bioinformatics in Cancer Research. Journal of Biomedicine and Biotechnology (4), 217-230. ISSN:1110-7243. |
 |
|
|
|
| Berger, A (2004). Dynamics and digits: on the ubiquity of Benford’s law. pp 693-695 in: F. Dumortier, H. Broer, J. Mahwin, A. Vanderbauwhede, S. Verduyn Lunel (eds): Proceedings of Equadiff 2003. World Scientific. |
 |
|
|
|
| Berger, A (2005). Benford’s Law in power-like dynamical systems. Stoch. Dyn. 5, 587-607. ISSN:0219-4937. |
 |
|
|
|
| Berger, A (2005). Multi-dimensional dynamical systems and Benford's law. Discrete and Continuous Dynamical Systems 13(1), 219-237. ISSN:1078-0947. |
 |
|
|
|
| Berger, A (2011). Some dynamical properties of Benford sequences. Journal of Difference Equations and Applications 17(2), 137-159. |
 |
|
|
|
| Berger, A, Bunimovich, LA and Hill, TP (2005). One-dimensional dynamical systems and Benford's law. Transactions of the American Mathematical Society 357(1), 197-219. ISSN:0002-9947. |
 |
|
|
|
| Berger, A and Hill, TP (2007). Newton’s method obeys Benford’s law. American Mathematical Monthly 114 (7), 588-601. ISSN:0002-9890. |
 |
|
|
|
| Berger, A and Hill, TP (2010). Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law. University of Alberta preprint. |
 |
|
|
|
| Berger, A and Hill, TP (2011). Benford's Law Strikes Back: No Simple Explanation in Sight for Mathematical Gem. The Mathematical Intelligencer 33(1), 85-91. |
 |
|
|
|
| Berger, A and Hill, TP (2011). A basic theory of Benford's Law . Probability Surveys 8, 1-126 (2011) . |
 |
|
|
|
| Berger, A, Hill, TP and Morrison, KE (2008). Scale-Distortion Inequalities for Mantissas of Finite Data Sets. Journal of Theoretical Probability 21(1), 97-117. ISSN:0894-9840. |
 |
|
|
|
| Berger, A and Siegmund, S (2007). On the distribution of mantissae in nonautonomous difference equations. Journal of Difference Equations and Applications 13(8-9), 829-845. ISSN:1023-6198. |
 |
|
|
|
| Berleant, D, Cheong, MP, Chu,C, Guan,Y, Kamal,A, Shedble, G, Ferson,S and Peters, JF (2003). Dependable Handling of Uncertainty. Reliable Computing 9(6), 407-418. ISSN:1385-3139. |
 |
|
|
|
| Bhattacharya, S (2002). From Kautilya to Benford – Trends in Forensic and Investigative Accounting. 9th World Congress of Accounting Historians, Deakin University. |
 |
|
|
|
| Bhattacharya, S, Kumar, K and Smarandache, F (2005). Conditional probability of actually detecting a financial fraud – a neutrosophic extension to Benford’s law. International Journal of Applied Mathematics 17(1), 7-14. |
 |
|
|
|
| Block, HW and Savits, TH (2010). A General Example for Benford Data. The American Statistician 64(4), 335-339. |
 |
|
|
|
| Bonache, A, Moris, K and Maurice, J (2009). Risque associé à l'utilisation de la loi de Benford pour détecter les fraudes
dans le secteur de la mode. Munich Personal RePEc Archive (MPRA) Paper No. 15352, posted 26 May 2009. |
 |
|
|
|
| Boyle, J (1994). An Application of Fourier Series to the Most Significant Digit Problem. American Mathematical Monthly 101(9), 879-886. ISSN:0002-9890. |
 |
|
|
|
| Bradley, JR and Farnsworth, DL (2009). What is Benford's Law?. Teaching Statistics 31(1), 2-6. |
 |
|
|
|
| Brähler, G, Bensmann, M and Emke, AL (2010). Der Einsatz mathematisch-statistischer Methoden in der
digitalen Betriebsprüfung. Illmenauer Schriften zur Betriebswirtschaftslehre 4/2010. |
 |
|
|
|
| Brähler, G, Bensmann, M and Jakobi, HR (2011). Das Benfordsche Gesetz und seine Anwendbarkeit bei der digitalen Prüfung von Fahrtenbüchern. Ilmenauer Schriften zur Betriebswirtschaftslehre 3/2011. |
 |
|
|
|
| Breunig, C and Goerres, A (2011). Searching for Electoral Irregularities in an Established Democracy: Applying Benford’s Law Tests to Bundestag Elections in Unified Germany. Electoral Studies (to appear). |
 |
|
|
|
| Brooks, D (2002). Naked-Eye Quantum Mechanics:
Practical Applications of Benford's Law for Integer Quantities. Frequencies - The Journal of Size Law Applications, Special Paper #1, 1-8. |
 |
|
|
|
| Brown, P, Chua, A and Mitchell, J (2002). The influence of cultural factors on price clustering: Evidence from Asia–Pacific stock markets. Pacific-Basin Finance Journal, 10(3), 307-332. |
 |
|
|
|
| Brown, P and Mitchell, J (2008). Culture and stock price clustering: evidence from the peoples’ republic of China. Pacific-Basin Finance Journal 16(1), 95-120 . ISSN:0927-538X. |
 |
|
|
|
| Brown, RJC (2005). Benford's Law and the screening of analytical data: the case of pollutant concentrations in ambient air. Analyst 130(9), 1280-1285. ISSN:0002-2654. |
 |
|
|
|
| Brown, RJC (2007). The use of Zipf's law in the screening of analytical data: a step beyond Benford. Analyst 132(4), 344-349. ISSN:0003-2654. |
 |
|
|
|
| Brunell, TL and Glazer, A (2001). Rational Response to Irrational Attitudes: The Level of the Gasoline Tax in the United States. Journal of Policy Analysis and Management 20(4), 761-769. ISSN:0276-8739. |
 |
|
|
|
| Buck, B, Merchant, AC and Perez, SM (1993). An illustration of Benford’s first digit law using alpha decay half lives. European Journal of Physics 14, 59-63. |
 |
|
|
|
| Burke, J and Kincanon, E (1991). Benford Law and Physical Constants - The Distribution of Initial Digits. American Journal of Physics 59 (10), 952. ISSN:0002-9505. |
 |
|
|
|
| Burns, B (2009). Sensitivity to statistical regularities: People (largely) follow Benford’s law. pp 2872-2877 in: Proceedings of CogSci 2009, Amsterdam, The Netherlands. |
 |
|
|
|
| Busta, B and Sundheim, R (1992). Tax return numbers tend to obey Benford's law. Center for Business Research Working Paper No. W93-106-94, St. Cloud State University, Minnesota. |
 |
|
|
|
| Busta, B and Sundheim, R (1992). Detecting manipulated tax returns with the use of Benford's Law. Center for Business Research Working Paper W95-106-94, St. Cloud State University, Minnesota. |
 |
|
|
|
| Busta, B and Weinberg, R (1998). Using Benford’s law and neural networks as a review procedure. Managerial Auditing Journal 13(6), 356-366. |
 |
|
|
|
| Buyse, M, George, SL and et al. (1999). The Role of Biostatistics in the Prevention, Detection and Treatment of Fraud in Clinical Trials. Statistics in Medicine 18 (24), 3435-3451. ISSN:0277-6715. |
 |
|
|
|
| Byalko, AV (1991). Statistics of Coefficients in Physical Formulas. Theoretical and Mathematical Physics 88(1), 782-787. ISSN:0040-5779. |
 |
|
|
|
| Cáceres, JLH, García, JLP and et al. (2008). First digit distribution in some biological data sets. Possible explanations for departures from Benford's Law. Electronic J Biomed 1, 27-35. |
 |
|
|
|
| Casey, MC (2004). Integrated Learning in Multi-net Systems. University of Surrey Ph.D. Thesis submitted Feb 2004. |
 |
|
|
|
| Chaitin-Chatelin, F (1994). Le calcul sur ordinateur a precision finie. Theorie et etat de l’art. CERFACS REPORT TR/PA/94/05. |
 |
|
|
|
| Chaitin-Chatelin, F (1995). Le calcul qualitatif. Comment donner un sens a des resultats faux?. CERFACS REPORT TR/PA/95/10. |
 |
|
|
|
| Chaitin-Chatelin, F (1996). Is finite precision arithmetic useful for physics?. Journal of Universal Computer Science 2(5), 380-395. |
 |
|
|
|
| Chaitin-Chatelin, F and Frayssé, V (1996). Lectures on Finite Precision Computations. SIAM. |
 |
|
|
|
| Chiverton, J and Wells, K (2006). Mixture effects in FIR low-pass filtered signals. IEEE Signal Processing Letters 13(6), 369-372. ISSN:1070-9908. |
 |
|
|
|
| Cho, WKT and Gaines, BJ (2007). Breaking the (Benford) law: Statistical fraud detection in campaign finance. American Statistician 61(3), 218-223. ISSN:0003-1305. |
 |
|
|
|
| Chou, MC, Kong, Q, Teo, CP, Wang, Z and Zheng, H (2009). Benford's Law and Number Selection in Fixed-Odds Numbers Game. Journal of Gambling Studies. |
 |
|
|
|
| Ciofalo, M (2009). Entropy, Benford’s first digit law, and the distribution of everything. Dipartimento di Ingegneria Nucleare, Università degli Studi di Palermo, Italy. |
 |
|
|
|
| Cleary, R and Thibodeau, JC (2005). Applying Digital Analysis Using Benford‘s Law to Detect Fraud: The Dangers of Type I Errors. Auditing - A Journal of Practice & Theory 24(1), 77-81. ISSN:0278-0380. |
 |
|
|
|
| Clenshaw, CV, Olver, FWJ and Turner, PR (1989). Level-Index Arithmetic - An Introductory Survey. Lecture Notes in Mathematics 1397, pp 95-168. ISSN:0075-8434. |
 |
|
|
|
| Cockshott, WP, McGregor, D and Wilson, J (1998). High-Performance Operations Using a Compressed Database Architecture. The Computer Journal 41(5), 283-296. ISSN:0010-4620. |
 |
|
|
|
| Cohen, DIA (1976). An Explanation of the First Digit Phenomenon. Journal of Combinatorial Theory Series A 20(3), 367-370. ISSN:0097-3165. |
 |
|
|
|
| Corazza, M, Ellero, A and Zorzi, A (2010). Checking financial markets via Benford's law: the S&P 500 case. pp 93-102 in: Corazza, M and Pizzi, C (Eds.): Mathematical and Statistical Methods for Actuarial Sciences and Finance, Springer. |
 |
|
|
|
| Costas, E, López-Rodas, V, Toro, FJ and Flores-Moya, A (2008). The number of cells in colonies of the cyanobacterium Microcystis aeruginosa satisfies Benford's law. Aquatic Botany 89(3), 341-343. |
 |
|
|
|
| Das, S and Zhang, H (2001). The stock market’s under-reaction to rounding-up in EPS. Preprint. |
 |
|
|
|
| Das, S and Zhang, H (2003). Rounding-up in reported EPS, behavioral thresholds, and earnings management. Journal of Accounting & Economics 35(1), 31-50. ISSN:0165-4101. |
 |
|
|
|
| Davis, B (1976). Some Remarks on Initial Digits. Fibonacci Quarterly 14(1), 13-14. ISSN:0015-0517. |
 |
|
|
|
| De Ceuster, MJK, Dhaene, G and Schatteman, T (1998). On the hypothesis of psychological barriers in stock markets and Benford’s law. Journal of Empirical Finance 5(3), 263-279. |
 |
|
|
|
| De Marchi, S and Hamilton, JT (2006). Assessing the accuracy of self-reported data: An evaluation of the toxics release inventory. Journal of Risk and Uncertainty 32(1), 57-76. ISSN:0895-5646. |
 |
|
|
|
| Dehaene, S and Mehler, J (1992). Cross-Linguistic Regularities in the Frequency of Number Words. Cognition 43(1), 1-29. ISSN:0010-0277. |
 |
|
|
|
| Diaconis, P (1977). The Distribution of Leading Digits and Uniform Distribution Mod 1. Annals of Probability 5(1), 72-81. ISSN:0091-1798. |
 |
|
|
|
| Diaconis, P and Freedman, D (1979). On Rounding Percentages. Journal of the American Statistical Association 74(366), 359-364. ISSN:0162-1459. |
 |
|
|
|
| Dickinson, JR (2002). A universal mathematical law criterion for algorithmic validity. Developments in Business Simulation and Experiential Learning 29, 26-33. |
 |
|
|
|
| Diekmann, A (2007). Not the First Digit! Using Benford's Law to Detect Fraudulent Scientific Data. Journal of Applied Statistics 34(3), 321-329. ISSN:0266-4763. |
 |
|
|
|
| Diekmann, A and Jann, B (2010). Benford’s Law and Fraud Detection: Facts and Legends. German Economic Review 11(3), 397–401. |
 |
|
|
|
| Diniz, JA, dos Santos, J, Dieng, M and Diniz, MAA (2006). Comprovação de Eficácia da Aplicação de Modelos Contabilométricos no Campo daAuditoria Digital das Contas Públicas Municipais: caso de um Tribunal de Contas de um estado brasileiro. |
 |
|
|
|
| Dlugosz, S and Müller-Funk, U (2009). The value of the last digit: statistical fraud detection with digit analysis. Advances in Data Analysis and Classification 3, 281-290. |
 |
|
|
|
| Docampo, S, del Mar Trigo, M, Aira, M, Cabezudo, B and Flores-Moya, A (2009). Benford’s law applied to aerobiological data and its potential as a quality control tool . Aerobiologia 25, 275-283 . ISSN:0393-5965. |
 |
|
|
|
| Dorfleitner, G and Klein, C (2009). Psychological barriers in European stock markets: Where are they?. Global Finance Journal 19(3), 268-285. |
 |
|
|
|
| Dorogovtsev, SN, Mendes, JFF and Oliveira, JG (2006). Frequency of occurrence of numbers in the World Wide Web. Physica A: Statistical Mechanics and its Applications 360(2), 548-556. ISSN:0378-4371. |
 |
|
|
|
| Dorrestijn, J (2008). Graphing conformity of distributions to Benford’s Law for various bases. MSc thesis, Universiteit Utrecht, The Netherlands. |
 |
|
|
|
| Dos Santos, J, Diniz, JA and Corrar, LJ (2005). O Foco é a Teoria Amostral nos Campos da Auditoria Contábil Tradicional e da Auditoria Digital: testando a Lei de Newcomb-Benford para o primeiro digito nas contas publicas. Brazilian Business Review 2 (1), 71-89. |
 |
|
|
|
| Doucouliagos, C (2004). Number preference in Australian stocks. Applied Financial Economics 14(1), 43-54. |
 |
|
|
|
| Doucouliagos, C (2005). Price exhaustion and number preference: time and price confluence in Australian stock prices. The European Journal of Finance 11(3), 207-222. |
 |
|
|
|
| Drake, PD and Nigrini, MJ (2000). Computer assisted analytical procedures using Benford’s law. Journal of Accounting Education 18, 127-146. |
 |
|
|
|
| Drmota, M and Tichy, RF (1997). Sequences, Discrepancies and Applications. Lecture Notes in Mathematics 1651. |
 |
|
|
|
| Dumas, CF and Devine, JH (2000). Detecting Evidence of Non-Compliance in Self-
Reported Pollution Emissions Data: An Application of Benford’s Law. Selected Paper, American Agricultural Economics Association, Annual meeting. |
 |
|
|
|
| Dümbgen, L and Leuenberger, C (2008). Explicit Bounds for the Approximation Error in Benford’s Law. Electronic Communications in Probability 13, 99-112. ISSN:1083-589X. |
 |
|
|
|
| Durrett, R (1996). Probability: Theory and Examples (2nd ed). p 301. |
 |
|
|
|
| Durtschi, C, Hillison, W and Pacini, C (2004). The effective use of Benford’s law to assist in detecting fraud in accounting data. Journal of Forensic Accounting 1524-5586/Vol. V, 17-34. |
 |
|
|
|
| Dworschak, M (1998). Weiter Weg zur Zwei. pp 228-229 in: Der Spiegel 47, 16 November. |
 |
|
|
|
| El Sehity, T, Hoelzl, E and Kirchler, E (2005). Price developments after a nominal shock: Benford's Law and psychological pricing after the euro introduction. International Journal of Research in Marketing 22(4), 471-480. ISSN:0167-8116. |
 |
|
|
|
| Engel, HA and Leuenberger, C (2003). Benford's law for exponential random variables. Statistics & Probability Letters 63, 361-365. ISSN:0167-7152. |
 |
|
|
|
| Fairthorne, RA (1969). Progress in Documentation - Empirical Hyperbolic Distributions (Bradford-Zipf-Mandelbrot) for Bibliometric Description and Prediction. Journal of Documentation 25(4), 319-343; reprinted 2005 in Journal of Documentation 61(2), 171-193. ISSN:0022-0418. |
 |
|
|
|
| Farkas, J and Gyürky, G (2010). The significance of using the Newcomb-Benford law as a test of nuclear half-life calculations. Acta Physica Polonica B 41, 1213-1221. ISSN:PL 0587-4254. |
 |
|
|
|
| Farnsworth, DF, Horan, KK and Galgon, RM (2007). A guide to Benford's law. Mathematics and Computer Education 41, 230-243. ISSN:ISSN: 0730-8639. |
 |
|
|
|
| Feldstein, A and Goodman, R (1976). Convergence Estimates for Distribution of Trailing Digits. Journal of the Association for Computing Machinery, 23(2), 287-297. ISSN:0004-5411. |
 |
|
|
|
| Feldstein, A and Turner, PR (1996). Overflow and underflow in multiplication and division. Applied Numerical Mathematics 21(3), 221-239. ISSN:0168-9274. |
 |
|
|
|
| Feldstein, A and Turner, PR (2006). Gradual and tapered overflow and underflow: A functional differential equation and its approximation. Applied Numerical Mathematics 56(3-4), 517-532. ISSN:0168-9274. |
 |
|
|
|
| Feller, W (1971). An Introduction to Probability Theory and Its Applications. p 63, vol 2, 2nd ed. J. Wiley. |
 |
|
|
|
| Fewster, RM (2009). A simple Explanation of Benford's Law. American Statistician 63(1), 20-25. |
 |
|
|
|
| Filipponi, P and Menicocci, R (1995). Some Probabilistic Aspects of the Terminal Digits of Fibonacci Numbers. Fibonacci Quarterly 33(4), 325-331. ISSN:0015-0517. |
 |
|
|
|
| Flehinger, BJ (1966). On the Probability that a Random Integer has Initial Digit A. American Mathematical Monthly 73(10), 1056-1061. ISSN:0002-9890. |
 |
|
|
|
| Frank, A (2006). Benford's law. http://reason-and-rhyme.blogspot.com/2006/10/benfords-law.html. |
 |
|
|
|
| Frey, B (2006). Spot Faked Data. Hack #64 in: Statistic Hacks, pp 251-262
O'Reilley Media, Sebastopol, CA. ISSN:ISBN-13: 978-0-596-1. |
 |
|
|
|
| Friedberg, SH (1984). The Distribution of First Digits. College Mathematics Journal 15(2), 120-125. ISSN:0049-4925. |
 |
|
|
|
| Frieden, BR (1999). F-Information, a Unitless Variant of Fisher Information. Foundations of Physics 29(10), 1521-1541. ISSN:0015-9018. |
 |
|
|
|
| Fu, D, Shi, YQ and Su, W (2007). A generalized Benford’s law for JPEG coefficients
and its applications in image forensics. Proceedings of SPIE, Volume 6505, Security, Steganography and Watermarking of Multimedia Contents IX, San Jose, California, January 28 - February 1, 2007. |
 |
|
|
|
| Garcia-Berthou, E and Alcaraz, C (2004). Incongruence between test statistics and P values in medical papers. BMC Medical Research Methodology 4(13). |
 |
|
|
|
| Gauvrit, N and Delahaye, JP (2008). A new general explanation of Benford’s law. Mathematiques et sciences humaines/ Mathematics and social sciences, 182, 7-15. |
 |
|
|
|
| Gauvrit, N and Delahaye, JP (2009). Scatter and regularity imply Benford's Law ... and more. arXive preprint. |
 |
|
|
|
| Gauvrit, N and Delahaye, JP (2009). Loi de Benford générale (General Benford Law). Mathématiques et sciences humaines/ Mathematics and Social Sciences 186, 5–15. |
 |
|
|
|
| Genolini, C and Driss, T (2010). Eveiller l'intérêt pour la statistique par l'exemple. Statistique et Enseignement 1(2), 49-57. |
 |
|
|
|
| Gent, I and Walsh, T (2001). Benford’s law. Preprint. APES Research Report, 2001. |
 |
|
|
|
| Geyer, CL and Williamson, PP (2004). Detecting Fraud in Data Sets Using Benford's Law. Communications in Statistics: Simulation and Computation 33(1), 229-246. ISSN:0361-0918. |
 |
|
|
|
| Giles, DE (2006). The Exact Asymptotic Distribution Function of Watson's UN2 for Testing Goodness-of-Fit with Circular Discrete Data. University of Victoria, Econometrics Working Paper EWP0607. ISSN:1485-6441. |
 |
|
|
|
| Giles, DE (2007). Benford's law and naturally occurring prices in certain eBay auctions. Applied Economics Letters 14(3), 157-161. ISSN:1350-4851. |
 |
|
|
|
| Giuliano, R and Janvresse, E (2010). A unifying probabilistic interpretation of Benford's Law. Uniform Distribution Theory. |
 |
|
|
|
| Göb, R (2007). Data Conformance Testing by Digital Analysis–A Critical Review and an Approach to More Appropriate Testing. Quality Engineering 19 (4), 281-297. |
 |
|
|
|
| Gonzalez-Garcia, J and Pastor, G (2009). Benford’s Law and Macroeconomic Data Quality. International Monetary Fund Working Paper WP/09/10, Statistics Department, January 2009. |
 |
|
|
|
| Good, IJ (1986). Some statistical applications of Poisson’s work. Statistical Science 1(2), 157-170. |
 |
|
|
|
| Goudsmit, SA (1977). Pitfalls in Elementary Probability. Proceedings of the American Philosophical Society 121(2), 188-189. ISSN:0003-049X. |
 |
|
|
|
| Goudsmit, SA and Furry, WH (1944). Significant figures of numbers in statistical tables. Nature 154(3921), 800-801. ISSN:0028-0836. |
 |
|
|
|
| Grabowski, F and Trojanowski, P (2006). Benford's law in image analysis. Tools of Information Technology, Rzeszow, 15 Sep 2006. |
 |
|
|
|
| Grandison, S and Morris, RJ (2008). Biological pathway kinetic rate constants are scale-invariant. Bioinformatics 24(6), 741-743. ISSN:1367-4803. |
 |
|
|
|
| Grendar, M, Judge, G and Schechter, L (2007). An empirical non-parametric likelihood family of data-based Benford-like distributions. Physica A: Statistical Mechanics and its Applications 380, 429-438. ISSN:0378-4371. |
 |
|
|
|
| Griffiths, TL and Kalish, ML (2002). A multidimensional scaling approach to mental multiplication. Memory & Cognition 30(1), 97-106. ISSN:0090-502X. |
 |
|
|
|
| Groce, D (2005). Benford's Law. Presentation at the Lyncean Group, California, USA, 23 March. |
 |
|
|
|
| Guan, L, He, D and Yang, D (2006). Auditing, integral approach to quarterly reporting, and cosmetic earnings management. Managerial Auditing Journal 21(6), 569-581. |
 |
|
|
|
| Guan, L, Skousen, CJ and Wetzel, TS (2005). Unusual Patterns in Reported Earnings: Additional Evidence. Journal of Forensic Accounting 6(2), 317-332. |
 |
|
|
|
| Guillou, A and Hall, P (2001). A diagnostic for selecting the threshold in extreme value analysis. Journal of the Royal Statistical Society Series B - Statistical Methodology 63(2), 293-305. ISSN:1369-7412. |
 |
|
|
|
| Günnel, S and Tödter, KH (2009). Does Benford's law hold in economic research and forecasting?. Empirica 36, 273-292. |
 |
|
|
|
| Haber, S (1983). Parameters for Integrating Periodic Functions of Several Variables. Mathematics of Computation 41(163), 115-129. ISSN:0025-5718. |
 |
|
|
|
| Hafner, EM (1979). Circular slide roulette. IEEE Communications Magazine 17(2), 29-32. |
 |
|
|
|
| Haigh, J (2003). Benford's Law. pp 283-286 in: Taking Chances: Winning with Probability, Oxford University Press. |
 |
|
|
|
| Hales, DN, Sridharan, V, Radhakrishnan, A, Chakravorty, SS and Sihad, SM (2008). Testing the accuracy of employee-reported data: An inexpensive alternative approach to traditional methods. European Journal of Operational Research 189(3), 583-593. |
 |
|
|
|
| Hassan, B (2002). Assessing data authenticity with Benford’s law. Information Systems Control Journal 6. |
 |
|
|
|
| Hassan, B (2003). Examining data accuracy and authenticity with leading digit frequency analysis. Industrial Management & Data Systems 103(1-2), 121-125. ISSN:0263-5577. |
 |
|
|
|
| Havil, J (2003). Benford's Law. Sec 14.2, pp 145-155 in: Gamma: Exploring Euler's Constant, Princeton University Press, USA. |
 |
|
|
|
| Havil, J (2008). Benford's Law. pp 190-200 in: Impossible? Surprising solutions to counterintuitive conundrums, Princeton University Press, USA. ISSN:ISBN 978-0-691-13131. |
 |
|
|
|
| Hayes, S (2009). Benford’s law in relation to terminal digit preference. Journal of Clinical Pathology 62(6), 575-576. |
 |
|
|
|
| Herrmann, D and Thomas, WB (2005). Rounding of Analyst Forecasts. Accounting Review 80(3), 805-823. ISSN:0001-4826. |
 |
|
|
|
| Hesman, T (1999). Randomness rules. The Dallas Morning News, August 9. |
 |
|
|
|
| Hickman, MJ and Rice, SK (2010). Digital Analysis of Crime Statistics: Does Crime Conform to Benford’s Law?. Journal of Quantitative Criminology 26(3), 333-349. |
 |
|
|
|
| Hill, TP (1988). Random-Number Guessing and the First Digit Phenomenon. Psychological Reports 62(3): 967-971. ISSN:0033-2941. |
 |
|
|
|
| Hill, TP (1995). A Statistical Derivation of the Significant-Digit Law. Statistical Science 10(4), 354-363. ISSN:0883-4237. |
 |
|
|
|
| Hill, TP (1995). The Significant-Digit Phenomenon. American Mathematical Monthly 102(4), 322-327. ISSN:0002-9890. |
 |
|
|
|
| Hill, TP (1995). Base-Invariance Implies Benford's Law. Proceedings of the American Mathematical Society 123(3), 887-895. ISSN:0002-9939. |
 |
|
|
|
| Hill, TP (1996). A note on distributions of true versus fabricated data. Perceptual and Motor Skills 83, 776-778 Part 1. ISSN:0031-5215. |
 |
|
|
|
| Hill, TP (1997). Benford law. Encyclopedia of Mathematics Supplement, vol. 1, 102-103. |
 |
|
|
|
| Hill, TP (1998). The First-Digit Phenomenon. American Scientist 86 (4), 358-363. ISSN:0003-0996. |
 |
|
|
|
| Hill, TP (1999). Le premier chiffre significatif fait sa loi. La Recherche Hors Serie 316, 72-74. |
 |
|
|
|
| Hill, TP (1999). The difficulty of faking data. Chance 12(3), 27-31. |
 |
|
|
|
| Hobza, T and Vajda, I (2001). On the Newcomb-Benford law in models of statistical data. Revista Matematica Complutense XIV(2), 407-420. ISSN:1139-1138. |
 |
|
|
|
| Horn, B, Kreuzer, M, Kochs, EF and Schneider, G (2006). Different states of anesthesia can be detected by Benford's Law. Journal of Neurosurgical Anesthesiology 18(4), 328-329. |
 |
|
|
|
| Hoyle, DC, Rattray, M, Jupp, R and Brass, A (2002). Making sense of microarray data distributions. Bioinformatics 18(4), 576-584. ISSN:1367-4803. |
 |
|
|
|
| Hsü, EH (1948). An Experimental Study on "Mental Numbers" and a New Application. The Journal of General Psychology 38, 57-67. |
 |
|
|
|
| Huang, SM, Yen, DC, Yang, LW and Hua, JS (2008). An investigation of Zipf's Law for fraud detection. Decision Support Systems 46(1), 70-83. |
 |
|
|
|
| Hubert, JJ (1981). General Bibliometric Models. Library Trends 30(1), 65-81. ISSN:0024-2594. |
 |
|
|
|
| Humenberger, H (1996). Das Benford-Gesetz über die Verteilung der ersten Ziffer von Zahlen. Stochastik in der Schule 16(3), 2–17. |
 |
|
|
|
| Humenberger, H (2008). Eine elementarmathematische Begründung des Benford-Gesetzes. Der Mathematikunterricht 54(1), 24-34. |
 |
|
|
|
| Hungerbühler, N (2007). Benfords Gesetz über führende Ziffern: Wie die Mathematik Steuersündern das Fürchten lehrt. EducETH. |
 |
|
|
|
| Hürlimann, W (2009). Generalizing Benford’s law using power laws: application to integer sequences. International Journal of Mathematics and Mathematical Sciences, Article ID 970284, 10 p. |
 |
|
|
|
| Huxley, SJ (2001). Why Benford's Law works and How to do digit analysis on spreadsheets. University of San Francisco website. |
 |
|
|
|
| Irmay, S (1997). The relationship between Zipf's law and the distribution of first digits. Journal of Applied Statistics 24(4), 383-393. ISSN:0266-4763. |
 |
|
|
|
| Iyengar, SS, Rajagopal, AK and Uppuluri, VRR (1983). String Patterns of Leading Digits. Applied Mathematics and Computation 12(4), 321-337. ISSN:0096-3003. |
 |
|
|
|
| Jamain, A (2001). Benford’s Law. Master Thesis. Imperial College of London and ENSIMAG. |
 |
|
|
|
| Jang, D, Kang, JU, Kruckman, A, Kudo, J and Miller, SJ (2008). Chains of distributions, hierarchical Bayesian models and Benford's Law. Journal of Algebra, Number Theory: Advances and Applications 1(1), 37-60. |
 |
|
|
|
| Jann, B (2008). Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples. The Stata Journal 8(2), 147-169. |
 |
|
|
|
| Janvresse, E (2009). Quel est le début de ce nombre ?. Images des Mathématiques, 26 December. |
 |
|
|
|
| Janvresse, E and de la Rue, T (2004). From Uniform Distributions to Benford’s Law. Journal of Applied Probability 41(4), 1203-1210. ISSN:0021-9002. |
 |
|
|
|
| Jasak, Z (2010). Benfordov zakon i reinforcement učenje (Benford's Law and reinforcment learning)
. MSc Thesis, University of Tuzla, Bosnia. |
 |
|
|
|
| Jasak, Z and Banjanovic-Mehmedovic, L (2008). Detecting Anomalies by Benford's Law. pp 453-458 in: IEEE International Symposium on Signal Processing and Information Technology, 2008. ISSPIT 2008. ISSN:978-1-4244-3554-8. |
 |
|
|
|
| Johnstone, P and Petry, FE (1994). Design and Analysis of Nonbinary Radix Floating-Point Representations. Computers & Electrical Engineering 20(1), 39-50. ISSN:0045-7906. |
 |
|
|
|
| Jolion, JM (2001). Images and Benford's Law. Journal of Mathematical Imaging and Vision 14(1), 73-81. ISSN:0924-9907. |
 |
|
|
|
| Judge, G and Schechter, L (2009). Detecting problems in survey data using Benford’s law. J. Human Resources 44, 1-24. |
 |
|
|
|
| Kafri, O (2007). The Second Law as a Cause of the Evolution. Preprint arXiv: 0711.4507, 2007 - arxiv.org. |
 |
|
|
|
| Kafri, O (2009). Entropy Principle in Direct Derivation of Benford's Law. arXiv:0901.3047v2. |
 |
|
|
|
| Khoshnevisan, M and Bhattacharya, S (2002). A short note on financial data set detection using neutrosophic probability. pp 74-79 in: Smarandache, F (ed), Proceedings of the first international conference on neutrosophy, neutrosophic logic, neutrosophic set, neutrosophic probability and statistics, University of New Mexico - Gallup, Dec 2001. |
 |
|
|
|
| Kinnunen, J and Koskela, M (2003). Who Is Miss World in Cosmetic Earnings Management? A Cross-National Comparison of Small Upward Rounding of Net Income Numbers among Eighteen Countries. Journal of International Accounting Research 2, 39-68. |
 |
|
|
|
| Knudsen, T (2001). Zipf’s Law for Cities and Beyond - The Case of Denmark. American Journal of Economics and Sociology 60(1), 123-146. ISSN:0002-9246. |
 |
|
|
|
| Knuth, DE (1997). The Art of Computer Programming. pp 253-264, vol. 2, 3rd ed, Addison-Wesley, Reading, MA. |
 |
|
|
|
| Kontorovich, AV and Miller, SJ (2005). Benford's Law, Values of L-functions and the 3x+ 1 Problem. Acta Arithmetica 120(3), 269-297. ISSN:0065-1036. |
 |
|
|
|
| Kossovsky, AE (2006). Towards a Better Understanding of the Leading Digits Phenomena. arXiv:math/0612627. |
 |
|
|
|
| Kozlov, VV (2005). Weighted averages, uniform distribution, and strict ergodicity. Russian Mathematical Surveys 60(6), 1121-1146. ISSN:0036-0279. |
 |
|
|
|
| Kreifelts, T (1973). Optimal Choice of Basis for a Floating-Point Arithmetic [Optimale Wahl für eine Gleitkomma-Arithmetik] . Computing 11(4), 353-363. ISSN:0010-485X. |
 |
|
|
|
| Kreiner, WA (2002). First digit law. Preprint, Universität Ulm. |
 |
|
|
|
| Kreiner, WA (2003). On the Newcomb-Benford Law. Zeitschrift für Naturforschung Section A - A Journal of Physical Sciences 58(11), 618-622. ISSN:0932-0784. |
 |
|
|
|
| Kumar, K and Bhattacharya, S (2007). Detecting the dubious digits: Benford’s law in forensic accounting. Significance 4(2), 81-83. |
 |
|
|
|
| Lagarias, JC and Soundararajan, K (2006). Benford's law for the 3x+1 function. Journal of the London Mathematical Society 74, 289-303. ISSN:0024-6107. |
 |
|
|
|
| Lebiere, C (1999). The dynamics of cognition: an ACT-R model of cognitive arithmetic. Kognitionswissenschaft 8(1), 5-19. |
 |
|
|
|
| Lee, J, Cho, WKT and Judge, G (2010). Stigler’s approach to recovering the distribution of first significant digits in natural data sets. Statistics and Probability Letters 80(2), 82-88. |
 |
|
|
|
| Leemis, LM and McQueston, JT (2008). Univariate distribution relationships. American Statistician 62(1), 45-53. ISSN:0003-1305. |
 |
|
|
|
| Leemis, LM, Schmeiser, BW and Evans, DL (2000). Survival Distributions Satisfying Benford's Law. American Statistician 54(4), 236-241. ISSN:0003-1305. |
 |
|
|
|
| Lei, S, Smith, M and Succi, G (2000). Empirical investigation of a novel approach to check the integrity of software engineering measuring processes. The 22nd International Conference on Software Engineering, Limerick, Ireland. |
 |
|
|
|
| Lemons, DS (1986). On the Numbers of Things and the Distribution of first Digits. American Journal of Physics 54(9): 816-817. ISSN:0002-9505. |
 |
|
|
|
| Ley, E (1996). On the Peculiar Distribution of the US Stock Indexes' Digits. American Statistician 50(4), 311-313. ISSN:0003-1305. |
 |
|
|
|
| Leydesdorff, L and Bensman, S (2006). Classification and powerlaws: The logarithmic transformation. Journal of the American Society for Information Science and Technology 57(11), 1470-1486. ISSN:1532-2882. |
 |
|
|
|
| Li, Z, Cong, L and Wang, H (2004). Discussion on Benford’s law and its application. http://arxiv.org/abs/math.ST/0408057. |
 |
|
|
|
| Lin, F, Chang, C and Wu, S (2009). A study on the relationship between related party transactions and monthly sales in Taiwan's publicly issued companies. to appear in: Journal of the Chinese Institute of Industrial Engineers. |
 |
|
|
|
| Lin, F, Guan, L and Fang, W (2009). Heaping In Reported Earnings: Evidence from Monthly Financial Reports of Taiwanese Firms. |
 |
|
|
|
| Lipovetsky, S (2008). Comparison among different patterns of priority vectors estimation methods. International Journal of Mathematical Education in Science 39(3), 301-311. |
 |
|
|
|
| Logan, JL and Goudsmit, SA (1978). The First Digit Phenomenon. Proceedings of the American Philosophical Society 122(4), 193-197. ISSN:0003-049X. |
 |
|
|
|
| Lolbert, T (2006). Digital Analysis: Theory and Applications in Auditing. Hungarian Statistical Review 84, Special number 10. ISSN:0039 0690. |
 |
|
|
|
| Lolbert, T (2007). Statisztikai eljárások alkalmazása az ellenőrzésben (Applications of statistical methods in monitoring). PhD thesis, Corvinus University, Budapest, Hungary. |
 |
|
|
|
| Lolbert, T (2008). On the non-existence of a general Benford's law. Mathematical Social Sciences 55(2), 103-106. ISSN:0165-4896. |
 |
|
|
|
| Lopez, J (2006). La prueba del último dígito. Prepint University of Texas El Paso. |
 |
|
|
|
| Lowe, T, Murphy, S and Hayward, J (1999). The first digit law. Preprint. |
 |
|
|
|
| Lu, F and Boritz, JE (2005). Detecting Fraud in Health Insurance Data: Learning to Model Incomplete Benford’s Law Distributions. Machine Learning: ECML 2005 (Proceedings). Lecture Notes in Artificial Intelligence 3270, 633-640. ISSN:0302-9743. |
 |
|
|
|
| Lu, OF and Giles, DE (2006). Benford's Law and Psychological Barriers in Certain eBay Auctions. Econometrics Working Paper EWP0606, University of Victoria. ISSN:1485-6441. |
 |
|
|
|
| Lu, T, Costello, CM, Croucher, PJP, Häsler, R, Deuschl, G and Schreiber, S (2005). Can Zipf's law be adapted to normalize microarrays?. BMC Bioinformatics 6, Art. No. 37. ISSN:1471-2105. |
 |
|
|
|
| Luque, B and Lacasa, L (2009). The first-digit frequencies of prime numbers and Riemann zeta zeros. Proc. Royal Soc. A, published online 22Apr09. |
 |
|
|
|
| Manoochehrnia, P, Rachidi, F, Rubinstein, M., Schulz, W. and Diefendorfer, G (2010). Benford’s Law and Its Application to Lightning Data. IEEE Transactions on Electromagnetic Compatibility, Vol. 52, Nr. 4, pp. 956-961, 2010.. |
 |
|
|
|
| Mansilla, R (2006). Análisis de los resultados electorales a partir de la Ley de Benford. preprint UNAM. |
 |
|
|
|
| Mardia, KV (1972). The distribution of first significant digits. pp 92-93 in: Statistics of Directional Data, Academic Press. |
 |
|
|
|
| Martín, AB (2003). Sistematización del proceso de depuración de los datos en estudios con seguimientos. PhD Thesis, Universitat Autònoma de Barcelona, Spain. |
 |
|
|
|
| Massé, B and Schneider, D (2011). A survey on weighted densities and their connection with the first digit phenomenon. Rocky Mountain Journal of Mathematics 41(5), 1395-1415. |
 |
|
|
|
| Matula, VV and Kornerup, P (1980). Foundations of Finite Precision Rational Arithmetic. pp 85-111 in: Alefeld, G, Grigorieff, RD (eds.) Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis), Computing Supplementum 2, Springer, Wien-New York. |
 |
|
|
|
| McCloskey, M, Harley, W and Sokol, SM (1991). Models of Arithmetic Fact retrieval - An Evaluation in Light of Findings from Normal and Brain-Damaged Subjects. Journal of Experimental Psychology - Learning Memory and Cognition 17(3), 377-397. ISSN:0278-7393. |
 |
|
|
|
| McLaughlin, WI and Lundy, SA (1984). Digit functions of integer sequences. Fibonacci Quarterly 22(2), 105-115. ISSN:0015-0517. |
 |
|
|
|
| Mendez, PF, Furrer, R, Ford, R and Ordóñez, F (2008). Scaling laws as a tool of materials informatics. JOM Journal of the Minerals, Metals and Materials Society 60(3), 60-66. ISSN:1047-4838. |
 |
|
|
|
| Mendez, PF and Ordonez, F (2005). Scaling Laws From Statistical Data and Dimensional Analysis. J. Appl. Mech. - Transactions of the ASME 72(5), 648-657. ISSN:0021-8936. |
 |
|
|
|
| Miller, SJ and Nigrini, MJ (2006). Order Statistics and Shifted Almost Benford Behavior. Preprint. |
 |
|
|
|
| Miller, SJ and Nigrini, MJ (2008). The Modulo 1 Central Limit Theorem and Benford's Law for Products. International Journal of Algebra 2(3), 119 - 130. |
 |
|
|
|
| Miller, SJ and Nigrini, MJ (2008). Order Statistics and Benford's Law. To appear in: International Journal of Mathematics and Mathematical Sciences. |
 |
|
|
|
| Miller, SJ and Takloo-Bighash, R (2006). An invitation to modern number theory. Princeton University Press. |
 |
|
|
|
| Miller, SJ and Takloo-Bighash, R (2007). Introduction to Random Matrix Theory. From: An Invitation to Modern Number Theory, Princeton University Press. |
 |
|
|
|
| Mir, TA (2011). Law of the leading digits and the ideological struggle for numbers. physics arXiv:1104.3948. |
 |
|
|
|
| Mir, TA (2011). The law of the leading digits and the world religions. Physica A: Statistical Mechanics and its Applications, 391 (2012), 792-798. |
 |
|
|
|
| Mir, TA (2012). The leading digit distribution of the worldwide illicit financial flows. arXiv:1201.3432. |
 |
|
|
|
| Mitchell, J (2001). Clustering and psychological barriers: the importance of numbers. Journal of Futures Markets 21(5), 395-428. ISSN:0270-7314. |
 |
|
|
|
| Mochty, L (2002). Die Aufdeckung von Manipulationen im Rechnungswesen - Was leistet das Benford's Law?. Die Wirtschaftsprüfung 14, 725-736. |
 |
|
|
|
| Moret, MA, de Senna, V, Pereira, MG and Zebende, GF (2006). Newcomb-Benford law in astrophysical sources. International Journal of Modern Physics C 17(11), 1597-1604. ISSN:0129-1831. |
 |
|
|
|
| Morrison, KE (2010). The Multiplication Game. Mathematics Magazine 83, 100-110. |
 |
|
|
|
| Morrow, J (2009). Benford's Law, Families of Distributions and a Test Basis. unpublished manuscript. |
 |
|
|
|
| Mörters, P (2001). Benford’s Gesetz über die Verteilung der Ziffern. Habilitationsvorlesung. Kaiserslauten und Bath. |
 |
|
|
|
| Mosimann, JE, Wiseman CV and Edelman RE (1995). Data fabrication: Can people generate random digits?. Accountability in Research: Policies and Quality Assurance 4(1), 31-55. |
 |
|
|
|
| Nagasaka, K (1984). On Benford's Law. Annals of the Institute of Statistical Mathematics 36(2), 337-352. ISSN:0020-3157. |
 |
|
|
|
| Nagasaka, K (2008). Benford’s Law to Base g of Order r in the Sense of a Certain Density. Short talk at: Colloque international sur la répartition uniforme, Marseille, January 2008. |
 |
|
|
|
| Nelson, LS (1984). Display Tables and Significant Digits. Journal of Quality Technology 16(3), 175-176. ISSN:0022-4065. |
 |
|
|
|
| Nguyen, HT, Kreinovich, V and Longpré, L (2003). Dirty pages of logarithm tables, lifetime of the universe, and subjective (fuzzy) probabilities on finite and infinite intervals. The 12th IEEE International Conference on Fuzzy Systems. FUZZ’03. Fuzzy Systems 1, 67-73. |
 |
|
|
|
| Nguyen, HT, Kreinovich, V and Longpré, L (2004). Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Innite Intervals. Reliable Computing 10(2), 83-106. |
 |
|
|
|
| Ni, D and Ren, Z (2008). Benford’s law and half-lives of unstable nuclei. Eur. Phys. J. A 38, 251–255. |
 |
|
|
|
| Ni, D, Wei, L and Ren, Z (2009). Benford's Law and β-Decay Half-Lives. Commun. Theor. Phys. 51, 713-716. |
 |
|
|
|
| Nigrini, MJ (1992). The Detection of Income Tax Evasion Through an Analysis of Digital Frequencies. PhD thesis, University of Cincinnati, OH, USA. |
 |
|
|
|
| Nigrini, MJ (1996). A taxpayer compliance application of Benford’s law. Journal of the American Taxation Association 18(1), 72-91. |
 |
|
|
|
| Nigrini, MJ (1999). Peculiar patterns of first digits. IEEE Potentials 18(2), 24-27. |
 |
|
|
|
| Nigrini, MJ (2000). Continuous Auditing. Preprint. |
 |
|
|
|
| Nigrini, MJ (2005). An Assessment of the Change in the Incidence of Earnings Management Around the Enron-Andersen Episode. Review of Accounting and Finance 4, 92-110. |
 |
|
|
|
| Nigrini, MJ and Miller, SJ (2007). Benford’s Law Applied to Hydrology Data—Results and Relevance to Other Geophysical Data. Mathematical Geology 39(5), 469-490. ISSN:0882-8121. |
 |
|
|
|
| Nigrini, MJ and Miller, SJ (2009). Data Diagnostics Using Second-Order Tests of Benford's Law. Auditing: A Journal of Practice & Theory 28(2), 305-324. |
 |
|
|
|
| Nigrini, MJ and Mittermaier, LJ (1997). The use of Benford's Law as an aid in analytical procedures. Auditing - A Journal of Practice & Theory 16(2), 52-67. ISSN:0278-0380. |
 |
|
|
|
| Niskanen, J and Keloharju, M (2000). Earnings cosmetics in a tax-driven accounting environment: evidence from Finnish public firms. European Accounting Review 9(3), 443-452. |
 |
|
|
|
| Nordtvedt, K (2001). Earth’s equivalence principle violating multipoles: more science from a robust violation signal in STEP . Classical and Quantum Gravity 18(13), 2467-2473. ISSN:0264-9381. |
 |
|
|
|
| Nye, J and Moul, C (2007). The Political Economy of Numbers: On the Application of Benford's Law to International Macroeconomic Statistics. The BE Journal of Macroeconomics 7(1). |
 |
|
|
|
| O'Brien, C (2003). Working Group on Methods on Fish Stock Assessments. ICES CM 2003/D:03 Ref. ACFM, G. |
 |
|
|
|
| Oleksy, M (2010). Data Mining und Benford's Law als Controllinginstrumente. Band 45, Wismarer Schriften zu Management und Recht, Europäischer Hochschulverlag, Bremen. ISSN:978-3867414-40. |
 |
|
|
|
| Olver, FWJ (1982). Further Developments of Rp and Ap Error Analysis. IMA Journal of Numerical Analysis 2(3), 249-274. ISSN:0272-4979. |
 |
|
|
|
| Oriol, JC (2007). Formation à la statistique par la pratique d'enquêtes par questionnaires et la simulation: étude didactique d'une experience d'enseignment dans u department d'IUT. Ph.D. Thesis, Université Lumière, Lyon, France. |
 |
|
|
|
| Oriol, JC and Regnier, JC (2007). La Loi de Benford et la Pratique d'enquêtes: Un Exemple de Situations Didactiques en Statistique Journees. Journées SFdS 2004. |
 |
|
|
|
| Orita, M, Moritomo, A, Niimi, T and Ohno, K (2010). Use of Benford’s law in drug discovery data. Drug Discovery Today 15(9/10), 328-331. |
 |
|
|
|
| Oteo, JA and Ros, J (2007). Double precision errors in the logistic map: Statistical study and dynamical interpretation. Physical Review E 76(3), Art. No. 036214. ISSN:1539-3755. |
 |
|
|
|
| Pain, JC (2008). Benford’s law and complex atomic spectra. Physical Review E 77(1): Art. No. 012102. ISSN:1539-3755. |
 |
|
|
|
| Pan, D, Shao, L and Ma, BQ (2010). Benford's Law in Statistical Physics. Wolfram Online Demonstrations Projects. |
 |
|
|
|
| Patil, N, Mahadevan, P and Chatterjee, A (2008). A constructive empirical theory for metal fatigue under block cyclic loading. Proceedings of the Royal Society A - Mathematical Physical and Engineering Sciences 464, 1161-1179. ISSN:1364-5021. |
 |
|
|
|
| Patil, SA and Uppuluri, VRR (1986). The distribution of first j digits. College Mathematical Journal 17(3), 240-243. |
 |
|
|
|
| Pavlov, AI (1982). On the distribution of fractional parts and Benford’s law. Math. USSR Izvestija 19(1), 65-77. English translation of: Izv. Akad. Nauk SSSR Ser. Mat., 1981, 45(4), 760–774. |
 |
|
|
|
| Perez-Gonzalez, F, Heileman, GL and Abdallah, CT (2007). Benford's Law in Image Processing. Image Processing, pp I-405 - I-408. ICIP 2007. IEEE International Conference. |
 |
|
|
|
| Périn, S (2007). The Constructal Nature of the Air Traffic System. Ch. 6 in: Bejan, A, Merkx, GW (eds): Constructal Theory of Social Dynamics, Springer 2007. |
 |
|
|
|
| Peters, JV (1981). An equivalent form of Benford's law. Fibonacci Quarterly 19(1), 74-76. ISSN:0015-0517. |
 |
|
|
|
| Peterson, I (1998). First Digits. Science News Online, Ivars Peterson's MathTrek, 27 June. |
 |
|
|
|
| Phillips, T (2009). Simon Newcomb and "Natural Numbers" (Benford's Law). American Mathematical Society Feature Column, Monthly Essays on Mathematical Topics. |
 |
|
|
|
| Pietronero, L, Tosatti, E, Tosatti, V and Vespignani, A (1998). The Uneven Distribution of Numbers in Nature. Arxiv preprint cond-mat/9808305, 1998 - arxiv.org. |
 |
|
|
|
| Pietronero, L, Tosatti, E, Tosatti, V and Vespignani, A (2001). Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf. Physica A - Statistical Mechanics and its Applications 293(1-2), 297-304. ISSN:0378-4371. |
 |
|
|
|
| Pike, DP (2008). Testing for the Benford property. SIAM Undergraduate Research Online (SIURO) 1, 10-19. |
 |
|
|
|
| Pinkham, RS (1961). On the Distribution of First Significant Digits. Annals of Mathematical Statistics 32(4), 1223-1230. ISSN:0003-4851. |
 |
|
|
|
| Pocheau, A (2006). The significant digit law: a paradigm of statistical scale symmetries . European Physical Journal B 49(4), 491-511. ISSN:1434-6028. |
 |
|
|
|
| Porta Mana, PGL, Månsson, A and Björk, G (2007). The Laplace-Jaynes approach to induction. arXiv preprint. |
 |
|
|
|
| Posch, PN (2004). Ziffernanalyse in der Fälschungsaufspürung. Benford’s Gesetz und Steuererklärungen in Theorie und Praxis. unpublished manuscript. |
 |
|
|
|
| Posch, PN (2008). A Survey on Sequences and Distribution Functions
satisfying the First-Digit-Law. Journal of Statistics & Management Systems 11(1), 1-19. |
 |
|
|
|
| Posch, PN and Kreiner, WA (2005). A general approach to digital analysis exemplified by stock market indices. unpublished manuscript. |
 |
|
|
|
| Posch, PN and Kreiner, WA (2006). Analysing digits for portfolio formation and index tracking. Journal of Asset Management 7(1), 69-80. |
 |
|
|
|
| Pustet, R (2004). Zipf and his heirs. Language Sciences 26(1), 1-25. ISSN:0388-0001. |
 |
|
|
|
| Raimi, RA (1969). The Peculiar Distribution of First Digits. Scientific American 221(6), 109-119. ISSN:0036-8733. |
 |
|
|
|
| Raimi, RA (1969). On Distribution of First Significant Figures. American Mathematical Monthly 76(4), 342-348. ISSN:0002-9890. |
 |
|
|
|
| Raimi, RA (1976). The First Digit Problem. American Mathematical Monthly 83(7), 521-538. ISSN:0002-9890. |
 |
|
|
|
| Raimi, RA (1985). The First Digit Phenomenon Again. Proceedings of the American Philosophical Society 129(2), 211-219. ISSN:0003-049X. |
 |
|
|
|
| Rajagopal, AK, Uppuluri, VRR, Scott, DS, Iyengar, SS and Yellayi, M (1984). New structural properties of strings generated by leading digits of 2N. Applied Mathematics and Computation 14(3), 221-244. |
 |
|
|
|
| Rauch, B, Brähler, G, Engel, S and Göttsche, M (2011). Fact and Fiction in EU-Governmental Economic Data. German Economic Review 12(3), 243-255. |
 |
|
|
|
| Regazzini, E (1982). La legge di Benford-Furlan come legge statistica (The Benford-Furlan law as a statistical law). Statistica 42(3), 351-370. |
 |
|
|
|
| Rieger, J (1993). Das Rätsel der ersten Ziffern. Frankfurter Allgemeine Zeitung, Oktober 20. |
 |
|
|
|
| Rodriguez, RJ (2004). First Significant Digit Patterns from Mixtures of Uniform Distributions. American Statistician 58(1), 64-71. ISSN:0003-1305. |
 |
|
|
|
| Rodriguez, RJ (2004). Reducing False Alarms in the Detection of Human Influence on Data. Journal of Accounting, Auditing & Finance 19(2), 141-158. |
 |
|
|
|
| Romero-Rochin, V (2009). A derivation of Benford's Law ... and a vindication of Newcomb. preprint arXiv:0909.3822. |
 |
|
|
|
| Rosenkrantz, RD (1977). Benford's Law. Example 3.6.6, pp 67-68 in: Inference, Method and Decision: Towards a Bayesian Philosophy of Science, Reidel Publishing Company, USA. |
 |
|
|
|
| Ross, KA (2011). Benford's Law, a growth industry. American Mathematical Monthly 118, 571-583. |
 |
|
|
|
| Roukema, BF (2009). Benford's Law Anomalies in the 2009 Iranian presidential election. preprint arXiv:0906.2789. |
 |
|
|
|
| Rücker, G (2003). Benford's Law in Medical Data Sets. presentation given at: 49th Biometric Conference of the German Region of theInternational Biometric Society at Wuppertal, March 2003. |
 |
|
|
|
| Ryder, P (2009). The Relationship Between the Newcomb-Benford Law and the Distribution of Rational Numbers. Zeitschrift für Naturforschung 64a, 615-617. |
 |
|
|
|
| Ryder, P (2009). Multiple origins of the Newcomb-Benford law: rational numbers, exponential growth and random fragmentation. Staats- und Universitätsbibliothek Bremen, Germany. |
 |
|
|
|
| Sambridge, M, Tkalčić, H and Jackson, A (2010). Benford's law in the Natural Sciences. Geophysical Research Letters 37 (2010) L22301, doi:10.1029/2010GL044830. |
 |
|
|
|
| Sambridge, M, Tkalcic, H and Arroucau, P (2011). Benford's Law of First Digits: From Mathematical Curiosity to Change Detector. Asia Pacific Mathematics Newsletter 1(4), October 2011, 1-6. |
 |
|
|
|
| Sánchez, JLH (2002). Analisis de la megacefalia demografica urbana mediante leyes de Zipf y de potencia
(Urban demographic analysis by using Zipf and potence laws). Theoria 11, 21-26. |
 |
|
|
|
| Sandron, F (2002). Do populations conform to the law of anomalous numbers?. Population 57(4/5), 753-761 (translated from French by SR Hayford). ISSN:1634-2941. |
 |
|
|
|
| Sarkar, BP (1973). An Observation on the Significant Digits of Binomial Coefficients and Factorials. Sankhya - The Indian Journal of Statistics Series B 35(3), 363-364. ISSN:0581-5738. |
 |
|
|
|
| Saville, A (2003). Using Benford's Law to predict data error and fraud. An examination of companies listed on the JSE securities exchange. |
 |
|
|
|
| Saville, A (2006). Using Benford's law to detect data error and fraud: an examination of companies listed on the Johannesburg Stock Exchange. South African Journal of Economic and Management Sciences 9(3), 341-354. ISSN:1015-8812. |
 |
|
|
|
| Schäfer, C, Schräpler, JP and Müller, KR (2004). Identification, Characteristics and Impact of Faked and Fraudulent Interviews in Surveys. |
 |
|
|
|
| Schäfer, C, Schräpler, JP, Müller, KR and Wagner GG (2004). Automatic Identification of Faked and Fraudulent Interviews in Surveys by Two Different Methods. Discussion paper 441, DIW Berlin (German Institute for Economic Research). |
 |
|
|
|
| Schatte, P (1987). On the Asymptotic Behaviour of the Mantissa Distributions of Sums. Journal of Information Processing and Cybernetics EIK 23(7), 353-360. |
 |
|
|
|
| Schatte, P (1988). On mantissa distributions in computing and Benford’s law. Journal of Information Processing and Cybernetics EIK 24(9), 443-455. |
 |
|
|
|
| Schatte, P (1988). On a law of the iterated logarithm for sums mod 1 with application to Benford's law. Probability Theory and Related Fields 77(2), 167-178. ISSN:0178-8051. |
 |
|
|
|
| Schatte, P (1989). On measures of uniformly distributed sequences and Benford's law. Monatshefte für Mathematik 107(3), 245-256. ISSN:0026-9255. |
 |
|
|
|
| Schatte, P (1998). On Benford's law to variable base. Statistics & Probability Letters 37(4): 391-397. ISSN:0167-7152. |
 |
|
|
|
| Scheidt, JK and Schelin, CW (1987). Distributions of floating point numbers. Computing 38(4), 315-324. ISSN:0010-485X. |
 |
|
|
|
| Schilling, MF (1992). Sequential Partitioning. American Mathematical Monthly 99(9), 846-855. ISSN:0002-9890. |
 |
|
|
|
| Schimmeck, T (1998). Eins zu null für Eins. Der Zufall mag manche Ziffern lieber als andere. Süddeutsche Zeitung Magazin Nr. 45, November 6. |
 |
|
|
|
| Schmidt, R and Lacher, R (1984). Probabilistic repeatability among some irrationals. College Mathematics Journal 15(4), 330-332. |
 |
|
|
|
| Schraepler, J-P (2010). Benford's Law as an instrument for fraud detection in surveys using the data of the Socio-Economic Panel (SOEP). Socio-Economic Panel (SOEP) paper No. 273, March 2, 2010.. |
 |
|
|
|
| Schräpler, JP and Wagner, GG (2003). Identification, characteristics and impact of faked interviews in surveys. An analysis by means of genuine fakes in the raw data of SOEP. IZA Discussion paper no. 969. Also published as DIW Berlin (German Institute for Economic Research) discussion paper 392, December 2003 - online at www.diw-berlin.de/documents/publikationen/73/41110/dp392.pdf. |
 |
|
|
|
| Schürger, K (2008). Extensions of Black-Scholes processes and Benford's law. Stochastic Processes and their Applications 118(7), 1219-1243. |
 |
|
|
|
| Scott, PD and Fasli, M (2001). Benford’s law: an empirical investigation and a novel explanation. CSM Technical Report 349, Department of Computer Science, University of Essex, UK. |
 |
|
|
|
| Scott, SK, Barnard, PJ and May, J (2001). Specifying executive representations and processes in number generation tasks. Quarterly Journal of Experimental Psychology, Section A - Human Experimental Psychology 54(3), 641-664. ISSN:0272-4987. |
 |
|
|
|
| Sen, A and Sen, U (2011). Benford's law detects quantum phase transitions similarly as earthquakes. EPL (Europhysics Letters) 95(5), 50008, 1-6. |
 |
|
|
|
| Sentance, WA (1973). A further analysis of Benford’s law. Fibonacci Quarterly 11, 490-494. |
 |
|
|
|
| Shao, L and Ma, BQ (2009). First Digit Distribution of Hadron full width. Modern Physics Letters A, 24(40), 3275-3282. |
 |
|
|
|
| Shao, L and Ma, BQ (2010). Empirical mantissa distributions of pulsars. Astroparticle Physics 33, 255-262. |
 |
|
|
|
| Shao, L and Ma, BQ (2010). The significant digit law in statistical physics. Physica A 389, 3109-3116. |
 |
|
|
|
| Shao, L and Ma, BQ (2010). First-digit law in nonextensive statistics. Physical Review E 82, 041110. |
 |
|
|
|
| Sharpe, MJ (2006). Limit Laws and Mantissa Distributions. Probability and Mathematical Statistics 26(1), 175-185. |
 |
|
|
|
| Shikano, S and Mack, V (2011). When does 2nd Digit Benford´s Law-Test signal an election fraud? Facts or misleading test results. Jahrbücher für Nationalökonomie und Statistik 231 (5+6), 719-732. |
 |
|
|
|
| Skousen, CJ, Guan, L and Wetzel, TS (2004). Anomalies and unusual patterns in reported earnings: Japanese managers round earnings. Journal of International Financial Management & Accounting 15(3), 212-234. |
 |
|
|
|
| Smilek, D, Carriere, JSA, Dixon, MJ and Merikle, PM (2007). Grapheme Frequency and Color Luminance in Grapheme-Color Synaesthesia. Psychological Science 18(9), 793-795. ISSN:0956-7976. |
 |
|
|
|
| Soffer, BH and Lynch, DK (1999). Some paradoxes, errors, and resolutions concerning the spectral optimization of human vision. American Journal of Physics 67(11), 946-953. ISSN:0002-9505. |
 |
|
|
|
| Stoschek, EP and Schönfeld, D (2002). Benford's Law - Places of interest near Benford`s Law. Module 45 of: Workshop on Design of Algorithms. |
 |
|
|
|
| Strzałka, D (2010). On some properties of Benford's law. Journal of the Korean Math. Soc. 47, 1055-1075. |
 |
|
|
|
| Sundheim, R and Busta, B (1993). Fibonacci numbers tend to obey Benford's law: an extension of Wlodarski and Sentance. Working Paper, St. Cloud State University, St. Cloud, Minnesota. |
 |
|
|
|
| Swanson, D, Cho, MJ and Eltinge, J (2003). Detecting possibly fraudulent or error-prone survey data using Benford’s law. pp 4172-4177 in: 2003 Joint Statistical Meetings - Section on Survey Research Methods, Proceedings of the American Statistical Association. |
 |
|
|
|
| Tabachnikov, S (2005). Geometry and Billiards. p 25 in: AMS Student Mathematical Library vol.30. |
 |
|
|
|
| Tarantola, A (2006). Benford Effect. pp 112-113 in: Elements for Physics: Quantities, Qualities, and Intrinsic Theories, Springer. |
 |
|
|
|
| Thomas, JK (1989). Unusual Patterns in Reported Earnings. Accounting Review 64(4), 773-787. ISSN:0001-4826. |
 |
|
|
|
| Tijms, H (2007). Falsified data and Benford’s law
. pp 193-197 in: Understanding Probability: Chance Rules in Everyday Life (2nd ed), Cambridge University Press. |
 |
|
|
|
| Tödter, KH (2009). Benford's Law as an Indicator of Fraud in Economics. German Economic Review 10(3), 339-351. |
 |
|
|
|
| Tolle, CR, Budzien, JL and LaViolette, RA (2000). Do dynamical systems follow Benford's law?. Chaos, 10(2), 331-336. ISSN:1054-1500. |
 |
|
|
|
| Torres, J, Fernandez, S, Gamero, A and Sola, A (2007). How do numbers begin? (The first digit law). European Journal of Physics 28(3), L17-L25. ISSN:0143-0807. |
 |
|
|
|
| Tsao, NK (1974). On the Distributions of Significant Digits and Roundoff Errors. Communications of the ACM 17(5), 269-271. ISSN:0001-0782. |
 |
|
|
|
| Turner, PR (1982). The Distribution of Leading Significant Digits. IMA Journal orf Numerical Analysis 2(4), 407-412. ISSN:0272-4979. |
 |
|
|
|
| Turner, PR (1984). Further Revelations on LSD. IMA Journal of Numerical Analysis 4(2), 225-231. ISSN:0272-4979. |
 |
|
|
|
| Turner, PR (1987). The distribution of l.s.d. and its implications for computer design. The Mathematical Gazette 71 (March), 26-31. |
 |
|
|
|
| Vajda, I, Veselý, A and Zvarova, J (2005). On the Amount of Information Resulting from Empirical and Theoretical Knowledge. Revista Matemática Complutense 18(2), 275-283. |
 |
|
|
|
| Valadier, M (2012). The Benford phenomenon for random variables. Discussion of Feller's way. arXiv:1203.2518. |
 |
|
|
|
| Valk, G (2004). Benford’s Law and Faking Data. The Pi, Volume 1, Spring 2004, Dept of Mathematics and Statistics, Georgia State University, Atlanta, USA. |
 |
|
|
|
| Volcic, A (1996). The First Digit Problem and Scale-Invariance. pp 329-340 in: P. Marcellini, G. Talenti and E. Vesentini (eds), Partial differential equations and applications: collected papers in honor of Carlo Pucci. Marcel Dekker. |
 |
|
|
|
| Wallace, WA (2002). Assessing the quality of data used for benchmarking and decision- making. The Journal of Government Financial Management 51(3), 16-22. |
 |
|
|
|
| Watrin, C, Struffert, R and Ullmann, R (2008). Benford’s Law: an instrument for selecting tax audit targets?. Review of Managerial Science 2(3), 219-237. |
 |
|
|
|
| Weisstein, EW (2003). Benford's Law. pp 181-182 in: CRC concise encyclopedia of mathematics, Chapman & Hall. |
 |
|
|
|
| Weisstein, EW (2009). Benford's Law. MathWorld (A Wolfram Web Resource). |
 |
|
|
|
| Wells, K, Chiverton, J, Partridge, M, Barry, M, Kadhem, H and Ott, B (2005). The Partial Volume Effect in PET/SPECT and Benford's Law. Nuclear Science Symposium Conference Record, 2005 IEEE, Vol. 3. |
 |
|
|
|
| Wells, K, Chiverton, J, Partridge, M, Barry, M, Kadhem, H and Ott, B (2007). Quantifying the Partial Volume Effect in PET Using Benford's Law. IEEE Transactions on Nuclear Science 54(5), 1616-1625 Part 1. ISSN:0018-9499. |
 |
|
|
|
| Wlodarski, J (1971). Fibonacci and Lucas Numbers tend to obey Benford’s law. Fibonacci Quarterly 9, 87-88. |
 |
|
|
|
| Wolff, H and Auffhammer, M (2006). Endogenous Choice OF Development Indicators: Are Development Countries Misclassified? Evidence from the HDI. Agricultural and Resource Economics, UC Berkeley, USA. |
 |
|
|
|
| Ylvisaker, D (1977). Test Resistance. Journal of the American Statistical Association 72(359), 551-556. ISSN:0162-1459. |
 |
|
|
|
| Zbrodoff, NJ (1995). Why is 9+7 harder than 2+3 - Strength and Interference as Explanations of the Problem-Size Effect. Memory & Cognition 23(6), 689-700. ISSN:0090-502X. |
 |
|
|
|