Benford’s law and geographical information – the example of OpenStreetMap

References

• Barrington-Leigh, C. and Millard-Ball, A., 2017. The world’s user-generated road map is more than 80% complete. PLoS ONE, 12 (8), e0180698. doi:10.1371/journal.pone.0180698.
   PubMed Web of Science ®Google Scholar
• Benford, F., 1938. The law of anomalous numbers. Proceedings of the American Philosophical Society, 78 (4), 551–572.
   Google Scholar
• Berger, A. and Hill, T.P., 2011a. A basic theory of Benford’s law. Probability Surveys, 8, 1–126. doi:10.1214/11-PS175.
   Google Scholar
• Berger, A. and Hill, T.P., 2011b. Benford’s law strikes back: no simple explanation in sight for mathematical gem. The Mathematical Intelligencer, 33 (1), 85–91. doi:10.1007/s00283-010-9182-3.
   Web of Science ®Google Scholar
• Bjorholm, S., et al. 2008. To what extent does Tobler’s 1st law of geography apply to macroecology? A case study using American plams (Aracaceae). BMC Ecology, 8 (11). doi:10.1186/1472-6785-8-11.
   PubMedGoogle Scholar
• Crocetti, E. and Randi, G., 2016. Using the Benford’s law as a first step to assess the quality of cancer registry data. Frontiers in Public Health, 4, 225. doi:10.3389/fpubh.2016.00225.
   PubMed Web of Science ®Google Scholar
• Deckert, J., Myagkov, M., and Ordeshook, P.C., 2011. Benford’s law and the detection of election fraud. Political Analysis, 19 (3), 245–268. doi:10.1093/pan/mpr014.
   Web of Science ®Google Scholar
• 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, 5, 11–34.
   Google Scholar
• Fewster, R.M., 2009. A simple explanation of Benford’s law. The American Statistician, 63 (1), 26–32. doi:10.1198/tast.2009.0005.
   Web of Science ®Google Scholar
• Formann, A.K., 2010. The Newcomb–Benford law in its relation to some common distributions. PLoS ONE, 5 (5), e10541. doi:10.1371/journal.pone.0010541.
   PubMed Web of Science ®Google Scholar
• Frank, A.U., 2007. Data quality ontology: an ontology for imperfect knowledge. Proceedings of the 8th Conference on Spatial Information Theory (COSIT), 406–420. Melbourne, Australia. doi:10.1007/978-3-540-74788-8_25.
   Google Scholar
• Furry, W.H. and Hurwitz, H., 1945. Distribution of numbers and distribution of significant figures. Nature, 155, 52–53. doi:10.1038/155052a0.
   Web of Science ®Google Scholar
• Gauvrit, N. and Delahaye, J.-P., 2009. Loi de Benford générale. Mathématiques et sciences humaines, 186, 5–15. doi:10.4000/msh.11034.
   Google Scholar
• Geyer, A. and Martí, J., 2012. Applying Benford’s law to volcanology. Geology, 40 (4), 327–330. doi:10.1130/G32787.1.
   Web of Science ®Google Scholar
• Goodchild, M.F. and Li, L., 2012. Assuring the quality of volunteered geographic information. Spatial Statistics, 1, 110–120. doi:10.1016/j.spasta.2012.03.002.
   Web of Science ®Google Scholar
• Goudsmit, S.A. and Furry, W.H., 1944. Significant figures of numbers in statistical tables. Nature, 154, 800–801. doi:10.1038/154800a0.
   Google Scholar
• Haklay, M., 2010. How good is volunteered geographical information? A comparative study of Open- StreetMap and Ordnance Survey datasets. Environment and Planning B, 37 (4), 682–703. doi:10.1068/b35097.
   Web of Science ®Google Scholar
• Hecht, B. and Moxley, E., 2009. Terabytes of Tobler: evaluating the first law in a massive, domain-neutral representation of world knowledge. Proceedings of the 9th Conference on Spatial Information Theory (COSIT), 88–105. Aber Wrac'h, France. doi:10.1007/978-3-642-03832-7_6.
   Google Scholar
• Hellinger, E., 1909. Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. Journal für die reine und angewandte Mathematik, 136, 210–271. doi:10.1515/crll.1909.136.210.
   Google Scholar
• Hill, T.P., 1995a. Base-invariance implies Benford’s law. Proceedings of the American Mathematical Society, 123 (3), 887–895.
   Web of Science ®Google Scholar
• Hill, T.P., 1995b. A statistical derivation of the significant-digit law. Statistical Science, 10 (4), 354–363. doi:10.1214/ss/1177009869.
   Web of Science ®Google Scholar
• Jolion, J.-M., 2001. Images and Benford’s law. Journal of Mathematical Imaging and Vision, 14 (1), 73–81. doi:10.1023/A:1008363415314.
   Web of Science ®Google Scholar
• Judge, G. and Schechter, L., 2009. Detecting problems in survey data using Benford’s law. The Journal of Human Resources, 44 (1), 1–24. doi:10.3368/jhr.44.1.1.
   Web of Science ®Google Scholar
• Klonner, C., et al. 2018. Capturing flood risk perception via sketch maps. ISPRS International Journal of Geo-Information, 7 (9), 359. doi:10.3390/ijgi7090359.
   Web of Science ®Google Scholar
• Kullback, S. and Leibler, R., 1951. On information and sufficiency. The Annals of Mathematical Statistics, 22 (1), 79–86. doi:10.1214/aoms/1177729694.
   Google Scholar
• Mayer, M., Heck, D.W., and Mocnik, F.-B., 2020. Shared mental models as a psychological explanation for converging mental representations of place – the example of OpenStreetMap. Proceedings of the 2nd International Symposium on Platial Information Science (PLATIAL’19), 43–50. Coventry, UK. doi:10.5281/zenodo.3628871.
   Google Scholar
• Miller, H.J., 2004. Tobler’s first law and spatial analysis. Annals of the Association of American Geographers, 94 (2), 284–289. doi:10.1111/j.1467-8306.2004.09402005.x.
   Web of Science ®Google Scholar
• Mir, T.A., Ausloos, M., and Cerqueti, R., 2014. Benford’s law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions. The European Physical Journal B, 87, 261. doi:10.1140/epjb/e2014-50525-2.
   Web of Science ®Google Scholar
• Mocnik, F.-B., et al., 2018. A grounding-based ontology of data quality measures. Journal of Spatial Information Science, 16, 1–25. doi:10.5311/JOSIS.2018.16.360.
   Google Scholar
• Mocnik, F.-B., 2018a. Linked open data vocabularies for semantically annotated repositories of data quality measures. Proceedings of the 10th International Conference on Geographic Information Science (Giscience), 50:1–50:7. Melbourne, Australia. doi:10.4230/LIPIcs.GISCIENCE.2018.50.
   Google Scholar
• Mocnik, F.-B., 2018b. The polynomial volume law of complex networks in the context of local and global optimization. Scientific Reports, 8, 11274. doi:10.1038/s41598-018-29131-0.
   PubMed Web of Science ®Google Scholar
• Mocnik, F.-B., et al. 2019. Shared data sources in the geographical domain—a classification schema and corresponding visualization techniques. ISPRS International Journal of Geo-Information, 8 (5), 242. doi:10.3390/ijgi8050242.
   Web of Science ®Google Scholar
• Mocnik, F.-B., Westerholt, R. 2021. The effect of tectonic plate motion on georeferenced long-term global datasets. International Journal of Applied Earth Observation and Geoinformation, 94, 102183. doi:10.1016/j.jag.2020.102183.
   Web of Science ®Google Scholar
• Mocnik, F.-B. and Frank, A.U., 2015. Modelling spatial structures. Proceedings of the 12th Conference on Spatial Information Theory (COSIT), 44–64. Santa Fe, NM, USA. doi:10.1007/978-3-319-23374-1_3.
   Google Scholar
• Mocnik, F.-B., Zipf, A., and Raifer, M., 2017. The OpenStreetMap folksonomy and its evolution. Geo- Spatial Information Science, 20 (3), 219–230. doi:10.1080/10095020.2017.1368193.
   Web of Science ®Google Scholar
• Neis, P., Goetz, M., and Zipf, A., 2012. Towards automatic vandalism detection in OpenStreetMap. ISPRS International Journal of Geo-Information, 1 (3), 315–332. doi:10.3390/ijgi1030315.
   Web of Science ®Google Scholar
• Newcomb, S., 1881. Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics, 4 (1), 39–40. doi:10.2307/2369148.
   Google Scholar
• Nigrini, M.J., 1996. A taxpayer compliance application of Benford’s law. The Journal of the American Taxation Association, 18 (1), 72–91.
   Google Scholar
• Nigrini, M.J. and Wells, J.T., 2012. Benford’s law. Applications for forensic accounting, auditing, and fraud detection. Hoboken, NY: Wiley. doi:10.1002/9781119203094.
   Google Scholar
• 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. doi:10.1080/09638180020017159.
   Google Scholar
• Pérez-González, F., Heileman, G.L., and Abdallah, C.T., 2007. Benford’s law in image processing. Pro- ceedings of the 14th IEEE International Conference on Image Processing, 405–408. San Antonio, TX, USA. doi:10.1109/ICIP.2007.4378977.
   Google Scholar
• Pinkham, R.S., 1961. On the distribution of first significant digits. The Annals of Mathematical Statistics, 32 (4), 1223–1230. doi:10.1214/aoms/1177704862.
   Google Scholar
• Poiani, T.H., et al., 2016. Potential of collaborative mapping for disaster relief: a case study of Open- StreetMap in the Nepal earthquake 2015. Proceedings of th 49th Hawaii International Conference on System Sciences, 188–197. Koloa, HI, USA. doi:10.1109/HICSS.2016.31.
   Google Scholar
• Raifer, M., et al., 2019. OSHDB: a framework for spatio-temporal analysis of OpenStreetMap history data. Open Geospatial Data, Software and Standards, 4 (3). doi:10.1186/s40965-019-0061-3.
   Google Scholar
• Raimi, R.A., 1976. The first digit problem. The American Mathematical Monthly, 83 (7), 521–538. doi:10.1080/00029890.1976.11994162.
   Web of Science ®Google Scholar
• Raimi, R.A., 1985. The first digit problem again. Proceedings of the American Philosophical Society, 129 (2), 211–219.
   Web of Science ®Google Scholar
• Rauch, B., et al. 2011. Fact and fiction in EU-governmental economic data. German Economic Review, 12 (3), 243–255. doi:10.1111/j.1468-0475.2011.00542.x.
   Web of Science ®Google Scholar
• Sandron, F., 2004. Les populations suivent-elles la loi des nombres anomaux? Population, 57, 753–761. doi:10.3917/pope.204.0753.
   Google Scholar
• Shi, J., Ausloos, M., and Zhu, T., 2018. Benford’s law first significant digit and distribution distances for testing the reliability of financial reports in developing countries. Physica A, 492, 878–888. doi:10.1016/j.physa.2017.11.017.
   Web of Science ®Google Scholar
• Skousen, C.J., Guan, L., and Wetzel, T.S., 2004. Anomalies and unusual patterns in reported earnings: Japanese managers round earnings. Journal of International Financial Management and Accounting, 15 (3), 212–234. doi:10.1111/j.1467-646X.2004.00108.x.
   Google Scholar
• Sottili, G., et al. 2012. Benford’s law in time series analysis of seismic clusters. Mathematical Geosciences, 44 (5), 619–634. doi:10.1007/s11004-012-9398-1.
   Web of Science ®Google Scholar
• Sui, D.Z., 2004. Tobler’s first law of geography: a big idea for a small world? Annals of the Association of American Geographers, 94 (2), 269–277. doi:10.1111/j.1467-8306.2004.09402003.x.
   Web of Science ®Google Scholar
• Thomas, J.K., 1989. Unusual patterns in reported earnings. The Accounting Review, 64 (4), 773–787.
   Web of Science ®Google Scholar
• Tobler, W.R., 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography, 46, 234–240. doi:10.2307/143141.
   Web of Science ®Google Scholar
• Tobler, W.R., 2004. On the first law of geography: a reply. Annals of the Association of American Geographers, 94 (2), 304–310. doi:10.1111/j.1467-8306.2004.09402009.x.
   Web of Science ®Google Scholar
• Truong, Q.T., Touya, G., and de Runz, C., 2018. Towards vandalism detection in OpenStreetMap through a data driven approach. Proceedings of the 10th International Conference on Geographic Information Science (GIScience), 61:1–61:7. Melbourne, Australia. doi:10.4230/LIPIcs.GIScience.2018.61.
   Google Scholar
• Wand, Y. and Wang, R.Y., 1996. Anchoring data quality dimensions in ontological foundations. Communications of the ACM, 39 (11), 86–95. doi:10.1145/240455.240479.
   Web of Science ®Google Scholar
• Ward, J.H., Jr, 1963. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58 (301), 236–244. doi:10.1080/01621459.1963.10500845.
   Web of Science ®Google Scholar
• Watrin, C., Struffert, R., and Ullmann, R., 2008. Benford’s law: an instrument for selecting tax audit targets? Review of Managerial Science, 2, 219–237. doi:10.1007/s11846-008-0019-9.
   Google Scholar
• Westerholt, R., et al. 2018. A statistical test on the local effects of spatially structured variance. International Journal of Geographical Information Science, 32 (3), 571–600. doi:10.1080/13658816.2017.1402914.
   Web of Science ®Google Scholar
• Westlund, H., 2013. A brief history of time, space, and growth: Waldow Tobler’s first law of geography revisited. The Annals of Regional Science, 51 (3), 917–924. doi:10.1007/s00168-013-0571-3.
   Web of Science ®Google Scholar
• Zaharis, A., et al. 2011. Lightweight steganalysis based on image reconstruction and lead digit distribution analysis. International Journal of Digital Crime and Forensics, 3 (4), 29–41. doi:10.4018/jdcf.2011100103.
   Google Scholar