| Sakai, H (1991). Frequency distribution of first digit among population. Jinko mondai kenkyu. [Journal of population problems] 47(3), 74-78.
|
 |
|
|
|
| Sambridge, M, Tkalčić, 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. ISSN:2010-3484.
|
|
|
|
|
| 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.
|
|
|
|
|
| Sanches, J and Marques, JS (2006). Image reconstruction using the Benford law. Proceedings of the IEEE International Conference on Image Processing, Atlanta, GA, October 2006, pp. 2029-2032. ISSN:1522-4880. DOI:10.1109/ICIP.2006.312845.
|
|
|
|
|
| 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.
|
|
|
|
|
| Sandouly, P (1998). Fraudes la preuve par 1. Jeune Afrique 1978, December 8.
|
|
|
|
|
| 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, Bömermann, H, Nauenburg, R, Wenzel, K, Müller, KR and Wagner, GG (2006). Qualitätssicherung des Faktors Interviewer für den Mikrozensus. pp 209-216 in: Kehlenbach, J, Rockmann, U (eds.): Amtliche Mikrodaten für die Sozial- und Wirtschaftswissenschaften, Forschungsdatenzentrum der Statistischen Landesämter: Beiträge zu den Nutzerkonferenzen des FDZ der Statistischen Landesämter 2005.
|
|
|
|
|
| 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 (1973). Zur Verteilung der Mantisse in der Gleitkommadarstellung einer Zufallsgröße (Distribution of Mantissa in Floating Point Diagram of Random Variable). Zeitschrift fur Angewandte Mathematik und Mechanik 53(8), 553-565. ISSN:0044-2267.
|
|
|
|
|
| Schatte, P (1981). On random variables with logarithmic mantissa distribution relative to several bases. Elektronische Informationsverarbeitung und Kybernetik 17(4/6), 293-295. ISSN:0013-5712.
|
|
|
|
|
| Schatte, P (1983). On sums modulo 2π of independent random variables. Math. Nachr. 110, 243-262.
|
|
|
|
|
| Schatte, P (1983). On H∞ -summability and the uniform distribution of sequences. Math. Nachr. 113, 237-243.
|
|
|
|
|
| Schatte, P (1984). On the asymptotic uniform distribution of sums reduced mod 1. Math. Nachr. 115, 275-281.
|
|
|
|
|
| Schatte, P (1986). On the Asymptotic Logarithmic Distribution of the Floating-Point Mantissas of Sums. Math. Nachr. 127, 7-20. ISSN:0025-584X.
|
|
|
|
|
| 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 (1987). Some estimates of the H∞ -uniform distribution. Monatshefte für Mathematik 103, 233-240.
|
|
|
|
|
| Schatte, P (1988). On mantissa distributions in computing and Benford’s law. Journal of Information Processing and Cybernetics EIK 24(9), 443-455. ISSN:0863-0593.
|
|
|
|
|
| Schatte, P (1988). On the uniform distribution of certain sequences and Benford’s law. Math. Nachr. 136, 271-273.
|
|
|
|
|
| Schatte, P (1988). On the Almost Sure Convergence of Floating-Point Mantissas and Benford Law. Math. Nachr. 135, 79-83. ISSN:0025-584X.
|
|
|
|
|
| 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 (1990). On Benford’s law for continued fractions. Math. Nachr. 148, 137-144.
|
|
|
|
|
| Schatte, P (1991). On a uniform law of the iterated logarithm for sums mod 1 and Benford’s law. Lithuanian Mathematical Journal 31(1), 133-142.
|
|
|
|
|
| Schatte, P (1998). On Benford's law to variable base. Statistics & Probability Letters 37(4): 391-397. ISSN:0167-7152.
|
|
|
|
|
| Schatte, P (2001). Briefe an die Herausgeber. Mitteilungen der Deutschen Mathematiker Vereinigung, 2/2001, pp 6-7.
|
|
|
|
|
| Schatte, P and Nagasaka, K (1991). A note on Benford’s law for second order linear recurrences with periodical coefficients. Z. Anal. Anwend. 10(2), 251-254.
|
|
|
|
|
| Scheidt, JK and Schelin, CW (1987). Distributions of floating point numbers. Computing 38(4), 315-324. ISSN:0010-485X.
|
|
|
|
|
| Schetnikov, AL and Schetnikova, AB (2002). Teaching and Research Seminar "The distribution of the first significant digits". Matematicheskoe obrazovanie (Mathematical Education), № 2(21), 2002, p. 107–123. (in Russian).
RUS
|
|
|
|
|
| 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.
|
|
|
|
|
| Schräpler, JP and Wagner, GG (2005). Characteristics and impact of faked interviews in surveys – An analysis of genuine fakes in the raw data of SOEP. Allgemeines Statistisches Archiv 89, 7-20.
|
|
|
|
|
| Schüpfer, G, Hein, J, Casutt, M, Steiner, L and Konrad, C (2012). Vom Finanz- sum Wissenschaftsbetrug [From financial to scientific fraud : methods to detect discrepancies in the medical literature]. Der Anaesthesist 61(6):537-42. ISSN:0003-2417. DOI:10.1007/s00101-012-2028-y.
GER
|
|
|
|
|
| Schürger, K (2008). Extensions of Black-Scholes processes and Benford's law. Stochastic Processes and their Applications 118(7), 1219-1243. ISSN:0304-4149.
|
|
|
|
|
| Schürger, K (2011). Lévy processes and Benford’s Law. Preprint.
|
|
|
|
|
| Scorse, J (2007). Does being a “top 10” worst polluter affect facility environmental releases? Evidence from the U.S. Toxic Release Inventory. Monterey Institute of International Studies Working Paper.
|
|
|
|
|
| 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.
|
|
|
|
|
| Scozzafava, R (1981). Un esempio concreto di probabilita non σ-additiva: la distribuzione della prima cifra significativa dei dati statistici. Boll. Un. Mat. Ital. A(5) 18(3), 403-410.
|
|
|
|
|
| Scozzafava, R (1981). Non conglomerability and the First Digit Problem. Statistica 41(4), 561-565.
|
|
|
|
|
| Seaman, RS (2002). The relevance of Benford's Law to background field errors in data assimilation. Australian Meteorological Magazine 51(1), 25-33. ISSN:0004-9743.
|
|
|
|
|
| Sebastiani, P, Gussoni, E, Kohane, IS and Ramoni, MF (2003). Statistical challenges in functional genomics. Statistical Science 18(1), 33-60.
|
|
|
|
|
| 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.
|
|
|
|
|
| Shallit, J (2003). What this country needs is an 18c piece. The Mathematical Intelligencer 25(2), 20-23.
|
|
|
|
|
| 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.
|
|
|
|
|
| Shengmin, Z and Wenchao, W (2010). Does Chinese Stock Indices Agree with Benford's Law?. 2010 International Conference on Management and Service Science (MASS), 24-26 Aug. 2010, Wuhan, Page(s): 1 - 3, doi: 10.1109/ICMSS.2010.5575999. ISSN:978-1-4244-5325-2.
|
|
|
|
|
| Shenton, LR (1968). Periodicity and density of modified Fibonacci sequences. Fibonacci Quarterly 6(2), 109-116.
|
|
|
|
|
| Sheynin, OB (1984). On the History of the Statistical Method in Astronomy. Archive for History of Exact Sciences 29(2), 151-199. ISSN:0003-9519.
|
|
|
|
|
| Shi, YQ (2009). First digit law and its application to digital forensics. In H. J. Kim, S. Katzenbeisser, & A.T.S. Ho (Eds.), Digital watermarking: Seventh International Workshop (IWDW ’08) (pp. 444–456). Berlin: Springer-Verlag. ISSN:978-3-642-04437-3.
|
|
|
|
|
| Shi, YQ and Fu, D (2011). Apparatus and method for a generalized benford's law analysis of DCT and JPEG coefficients. Patent 7940989 Issued on May 10, 2011.
|
|
|
|
|
| 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.
|
|
|
|
|
| Simonet, S, Monteleone, S and Diego, A (2007). Analyse von Bildflächen auf Benfordverteilung am Beispiel von Northern Blots. ETH Zuerich sociology working paper.
|
|
|
|
|
| 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.
|
|
|
|
|
| Slijepčević, S (1998). A note on initial digits of recurrence sequences. Fibonacci Quarterly 36(4), 305-308.
|
|
|
|
|
| Slijepčević, S and Blašković, B (2013). Statistical detection of fraud in the reporting of Croatian public companies. Financial Theory and Practice, 38(1), pp. 81-96. DOI:10.3326/fintp.38.1.4.
|
|
|
|
|
| Sloane, NJA (2003). Sequences A055439 - A055449. in: The On-Line Encyclopedia of Integer Sequences (www.research.att.com/~njas/sequences/).
|
|
|
|
|
| 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.
|
|
|
|
|
| Smith, CA (2002). Detecting Anomalies in Your Data Using Benford’s Law. Paper 249 (Statistics and Data Analysis) in: Proceedings of SUGI 27, Orlando, USA, April 14-17.
|
|
|
|
|
| Smith, SW (1997). Explaining Benford's Law. Chapter 34 in: The Scientist and Engineer's Guide to Digital Signal Processing. California Technical Publishing: San Diego, CA. ISBN 0-9660176-3-3. Republished in softcover by Newnes, 2002.
|
|
|
|
|
| Snyder, MA, Curry, JH and Dougherty, AM (2001). Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law. Physical Review E 64(2), Art. No. 026222. ISSN:1063-651X.
|
|
|
|
|
| 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.
|
|
|
|
|
| Sornette, D (2002). Why stock markets crash: critical events in complex financial systems. Princeton University Press.
|
|
|
|
|
| Sottili, G, Palladino, DM, Giaccio, B and Messina, P (2012). Benford's Law in Time Series Analysis of Seismic Clusters. Mathematical Geosciences Volume 44, Number 5 (2012), 619-634, doi: 10.1007/s11004-012-9398-1.
|
|
|
|
|
| Sporring, J (1997). A prior of saliency based pruning algorithms. Technical report DIKU-97/8, Department of Computer Science, University of Copenhagen, Denmark.
|
|
|
|
|
| Stadje, W (2005). Asymptotic properties of digit sequences of random numbers. Mathematische Nachrichten 278(10), 1209-1229.
|
|
|
|
|
| Stanek, S (2000). Applying Benford's Law to internal audit. KnowledgeSpace, 14 August.
|
|
|
|
|
| Steutel, F (2009). De wet van Benford. STAtOR 10(1), 22-23.
|
|
|
|
|
| Stewart, I (1994). Das Gesetz der ersten Ziffer. Mathematische Unterhaltungen, in: Spektrum der Wissenschaft (April), 16-20.
|
|
|
|
|
| Stewart, I (2008). The Most Likely Digit. pp 106-109 in: Professor Stewart's Cabinet of Mathematical Curiosities, Basic Books, New York.
|
|
|
|
|
| Stigler, SM (1978). Mathematical Statistics in the Early States. Annals of Statistics 6(2), 239-265. ISSN:0090-5364.
|
|
|
|
|
| Stoschek, EP and Schönfeld, D (2002). Benford's Law - Places of interest near Benford`s Law. Module 45 of: Workshop on Design of Algorithms.
|
|
|
|
|
| Strauch, O (2012). Unsolved Problems. Uniform Distribution Theory, Unsolved Problems Section on the home-page of Uniform Distribution Theory. ISSN:1336-913X.
|
|
|
|
|
| Strzałka, D (2010). On some properties of Benford's law. Journal of the Korean Math. Soc. 47, 1055-1075.
|
|
|
|
|
| Suh, I and Headrick, TC (2010). A comparative analysis of the bootstrap versus traditional statistical procedures applied to digital analysis based on Benford's Law. Journal of Forensic and Investigative Accounting 2(2), 2010, 144-175.
|
|
|
|
|
| Suh, I, Headrick, TC and Minaburo, S (2011). An Effective and Efficient Analytic Technique: A Bootstrap Regression Procedure and Benford's Law. Journal of Forensic & Investigative Accounting, Vol.3, No. 3.
|
|
|
|
|
| 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.
|
|
|
|
|
| Szewczak, ZS (2010). A limit theorem for random sums modulo 1. Statistics & Probability Letters.
|
|
|
|
|
| Szpiro, G (2009). Neues aus dem Reich der Primzahlen. Neue Zürcher Zeitung, 27 Mai.
|
|
|
|
|