scholarly journals Some New Tests of Conformity with Benford’s Law

Stats ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 745-761
Author(s):  
Roy Cerqueti ◽  
Claudio Lupi
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Explicit Representation ◽  
Asymptotic Distributions ◽  
Benford’S Law ◽  
Test Statistics ◽  
Target Distribution ◽  
Benford's Law ◽  
Novel Devices

This paper presents new perspectives and methodological instruments for verifying the validity of Benford’s law for a large given dataset. To this aim, we first propose new general tests for checking the statistical conformity of a given dataset with a generic target distribution; we also provide the explicit representation of the asymptotic distributions of the relevant test statistics. Then, we discuss the applicability of such novel devices to the case of Benford’s law. We implement extensive Monte Carlo simulations to investigate the size and the power of the introduced tests. Finally, we discuss the challenging theme of interpreting, in a statistically reliable way, the conformity between two distributions in the presence of a large number of observations.

Selecting Audit Samples Using Benford's Law

2012 ◽  
Vol 32 (2) ◽  
pp. 53-65 ◽  
Author(s):  
Carlos Gomes da Silva ◽  
Pedro M. R. Carreira
Keyword(s):  
Mathematical Programming ◽  
Simulated Data ◽  
The Other ◽  
Programming Models ◽  
Benford’S Law ◽  
Digital Analysis ◽  
Test Statistics ◽  
Typical Data ◽  
Benford's Law ◽  
Contamination Levels

SUMMARY: We contribute to digital analysis by developing two mathematical programming models that can assist auditors in selecting more promising audit samples, using Benford's law. One model identifies the smallest subset of nonconforming records in a dataset, given some predefined conformity criteria, and the other highlights the k most nonconforming records. The models take into account several conformity tests and test statistics simultaneously. The application of the models is illustrated using suggested protocols on a set of simulated data. Finally, the effectiveness of the models in detecting typical data manipulations is assessed under different contamination levels.

scholarly journals Fraud Detection in Financial Statements Applying Benford's Law with Monte Carlo Simulation

2019 ◽  
Vol 69 (2) ◽  
pp. 217-239
Author(s):  
Vladan Pavlović ◽  
Goranka Knežević ◽  
Marijana Joksimović ◽  
Dušan Joksimović
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Frequency Distribution ◽  
High Probability ◽  
Financial Statements ◽  
Financial Statement ◽  
Benford’S Law ◽  
Financial Reports ◽  
Benford's Law ◽  
Very High

Benford's Law is a useful tool for detecting fraud in financial statements. In this paper we test the financial item named ‘Work performed by the undertaking for its own purpose and capitalised’ applying this tool. The data are taken from the financial reports of all companies submitted to the Serbian Business Register Agency for the period of 2008–2013. Our conclusion shows that there is a very high probability that the frequency distribution of the second digit does not satisfy Benford's Law. In other words, it implies that certain manipulations have been usually done with the second digit of the aforementioned item in the financial statement. This research confirms our hypothesis that financial statement frauds are usually conducted using the second digit.

Regression discontinuity designs with unknown state-dependent discontinuity points: estimation and testing

2018 ◽  
Vol 23 (2) ◽  
Author(s):  
Lixiong Yang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Treatment Effect ◽  
Regression Discontinuity ◽  
Test Statistics ◽  
State Dependency ◽  
Monte Carlo Experiments ◽  
State Dependent ◽  
Regression Discontinuity Designs ◽  
Biased Estimates

Abstract This paper extends Regression discontinuity designs with unknown discontinuity points developed by (Porter, J., and P. Yu. 2015. “Regression Discontinuity Designs with Unknown Discontinuity Points: Testing and Estimation.” Journal of Econometrics 189: 132–147.) to allow for state-dependent discontinuity points. We discuss the estimation of the model, and propose test statistics for treatment effect and state dependency in the discontinuity points. We conduct Monte Carlo simulations to compare the proposed estimator with these based on the constant discontinuity RDD and the classic fuzzy RDD, and find that overlooking the state dependency can lead to biased estimates of treatment effects, while the proposed estimator works well and is robust when applied to constant discontinuity RDDs. Monte Carlo experiments also point out that the sizes and powers of the proposed test statistics are generally satisfactory. The model is illustrated with an empirical application.

Low-voltage EDS of magnesium ferrite Dendrites in a FEG-SEM

1996 ◽  
Vol 54 ◽  
pp. 478-479
Author(s):  
Matthew T. Johnson ◽  
Ian M. Anderson ◽  
Jim Bentley ◽  
C. Barry Carter
Keyword(s):  
Monte Carlo ◽  
Quantitative Analysis ◽  
Monte Carlo Simulations ◽  
Cross Section ◽  
Spatial Resolution ◽  
Low Voltage ◽  
Magnesium Ferrite ◽  
X Ray ◽  
Interaction Volume ◽  
Ferrite Spinel

Energy-dispersive X-ray spectrometry (EDS) performed at low (≤ 5 kV) accelerating voltages in the SEM has the potential for providing quantitative microanalytical information with a spatial resolution of ∼100 nm. In the present work, EDS analyses were performed on magnesium ferrite spinel [(MgxFe1−x)Fe2O4] dendrites embedded in a MgO matrix, as shown in Fig. 1. spatial resolution of X-ray microanalysis at conventional accelerating voltages is insufficient for the quantitative analysis of these dendrites, which have widths of the order of a few hundred nanometers, without deconvolution of contributions from the MgO matrix. However, Monte Carlo simulations indicate that the interaction volume for MgFe2O4 is ∼150 nm at 3 kV accelerating voltage and therefore sufficient to analyze the dendrites without matrix contributions.Single-crystal {001}-oriented MgO was reacted with hematite (Fe2O3) powder for 6 h at 1450°C in air and furnace cooled. The specimen was then cleaved to expose a clean cross-section suitable for microanalysis.

MONTE CARLO SIMULATIONS OF ELECTRON DRIFT VELOCITIES IN THE NOBLE GASES AND THEIR MIXTURES

1979 ◽  
Vol 40 (C7) ◽  
pp. C7-63-C7-64
Author(s):  
A. J. Davies ◽  
J. Dutton ◽  
C. J. Evans ◽  
A. Goodings ◽  
P.K. Stewart
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Noble Gases ◽  
Electron Drift
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