Some aspects of the application of benford’s law in the analysis of the data set anomalies

Abstract

In this chapter the contemporary generally accepted theoretical analysis and assumptions regarding the implementation of Benford’s Law are presented. It seems interesting to introduce the perspective to Benford’s Law as a consequence of the universal law of nature stating that nature strives for the maximum entropy or disorder, as well as the perspective in which Benford’s Law, aspires to find its place in the contemporary theory of everything in nature. The implementation of this law in the analysis of the anomalies in some numerical data in various scientific disciplines is also part of this article. The incorrect numerical data that describes the specific occurrence can be the consequence of an unintentional error in the formation of the numerical data (as a consequence of bad design of an experiment, the imperfections of the detection of the numerical data, a badly set up model of some process that generates the set of numerical data, etc.), but also the consequence of intentional abuse. Using the Monte Carlo simulation, we determine the average values and standard deviation of the relative frequency of the first type error for the Mean Absolute Deviation test and for the Pearson X2 test of Benford’s Law, for the first digit, and the first two digits and we determine the acceptable length of series for the application of these tests, in the context of acceptable first type errors. We make the practical implementation of Benford’s Law by testing it on the data gathered from the International Monetary Fund, World Economic Outlook Database. We use two groups of data. The first group is the data regarding the Gross domestic product and the other group comprises the Current Account Balances for the 184 countries in the period from 1980 to 2016. The specific perspective provided in this chapter regards the implementation of this law in the forensic analysis of frauds, especially in the analysis of the numerical data that describes various sociological, econometrical and financial irregularities. We show how the mutual usage of Benford’s Law and specific laws of mathematical statistics, successfully detect potential irregularities in the numerical data and advances the forensic analyst’s potential fraud detection in this area.