Survival Distributions Satisfying Benford's Law

All Data are Wrong, but Some are Useful? Advocating the Need for Data Auditing

“…While the reliability of official fishery statistics has been widely questioned in the fisheries literature (see Watson and Pauly, 2001;Tesfamichael and Pauly, 2011;Pala, 2013;Pham et al, 2013;Pauly et al, 2014, and the references therein), our analysis provides further statistical evidence supporting the common belief that the reliability of the raw data themselves is the fundamental problem. In common with other Benford's law applications mentioned earlier (Nigrini, 1996;Leemis, Schmeiser, and Evans, 2000;Bolton and Hand, 2002;Cho and Gaines, 2007;Diekmann, 2007;de Marchi and Hamilton, 2006;Fewster, 2009;Graham, Hasseldine, and Paton, 2009;Judge and Schechter, 2009;Mebane, 2011), we emphasize however that this study does not provide conclusive evidence for the existence of fraud or misreporting, it only suggests that the anomalies identified in the data are compatible with their occurrence and further investigation is required.…”

“…It is a powerful probabilistic result which has been widely used for statistical fraud detection (Hill, 1995a;Nigrini, 1996;Leemis, Schmeiser, and Evans, 2000;Bolton and Hand, 2002;Cho and Gaines, 2007;Diekmann, 2007;de Marchi and Hamilton, 2006;Fewster, 2009;Graham, Hasseldine, and Paton, 2009;Judge and Schechter, 2009;Mebane, 2011) and as a simple, yet effective way to test for erroneous, fraudulent, and fabricated data (Cho and Gaines, 2007;Diekmann, 2007;Leemis, Schmeiser, and Evans, 2000;Ross, 2011). For example, Benford's law has been applied in contexts as diverse as tax auditing (Nigrini, 1996), survival analysis (Leemis, Schmeiser, and Evans, 2000), self-reported toxic emissions data (de Marchi and Hamilton, 2006), numerical analysis (Berger and Hill, 2007), scientific fraud detection (Diekmann, 2007), quality of survey data (Judge and Schechter, 2009), election fraud analysis (Mebane, 2011), and fraud detection in a commercial lobster fishery (Graham, Hasseldine, and Paton, 2009). This article's principal goal is to encourage the regular practice of performing a data audit when analyzing data or carrying out applied statistical research.…”

“…Two general justifications for assuming that Benford's law applies in a particular context are as follows: Hill (1995a,b) shows that Benford's law can be understood as a central-limit type theorem for significant digits, and Leemis, Schmeiser, and Evans (2000) show that Benford's law applies to a …”

Detecting Problems in Survey Data Using Benford's Law

“…We include the Pearson correlation coefficient between the empirical proportions of first digits in the data and those predicted by Benford. Additionally, as suggested by Leemis et al (2000), we calculate the distance measure m = max i=1,2,...,9 {|b i − e i |}. Third, as suggested by Cho & Gaines (2007) we include a measure which is based on the Euclidean distance be-…”

A first digit theorem for square-free integer powers

“…First of all, a reasonable GoF measure for the fitting of first-digit distributions should be size-dependent. This has been observed by Furlan [5], Section II.7.1, pp.70-71, who defines the ETA measure, and by Hürlimann [8], p.8, who applies the probability weighted least squares (WLS) measure used earlier by Leemis et al [12] (chi-square divided by sample size). Let 1 ), […”