Benford’s law is based on an observation that certain digits occur more often than others in a set of numbers. This have provided researchers to apply the law in different areas including identifying digit patterns and manipulated data. To our knowledge, this have yet not been tested in the Swedish housing market. The purpose of this thesis is to examine whether the sale price for 171 643 tenant-owned apartments in Stockholm, Gothenburg and Malmö follow Benford’s law. Numerous researchers have used this law for testing various types of data but based solely on the first digit distribution of their data. This study will furthermore test the second digit and the first two digits of our data. The tests used to evaluate our data’s conformity to Benford’s law include Kolmogorov-Smirnov test and Mean absolute deviation (MAD) test. We found that the second digit of sale prices did follow Benford’s law, the first digit and the first two digits did not follow the law. The results show that Benford’s law is a good method for identify certain digit patterns and further research is needed to draw the conclusion that sale price does not follow Benford’s law as certain limitations on our data was identified.

In response to the reported increase in accounting crime and suspected fraud in conjunction with the adjustment subsidies initialized during the covid-19 pandemic of 2020, we conducted a study examining accounting manipulation. Based on an explanatory theory for fraud, the Fraud Triangle, we theorize that the financial circumstances that companies experienced during the pandemic and the government subsidies created an environment where accounting manipulation could occur. We obtained a unique set of unpublished data from the Swedish Tax Agency. Two common models for detecting accounting manipulation were then applied to a large sample of Swedish companies. We used a version of the Jones Model to detect potential earnings management and Benford’s Law to detect fraudulent manipulation of the firms’ reported loss of revenue. Our results indicate earnings management and fraudulent reporting for some industries but no broad indication of systematic accounting manipulation across all industries. However, we suggest future research on this topic to further understand how accounting manipulation occurs in distressed industries.

我國全民健保近年財務不佳，民國98年收支短絀達582億元。根據中央健康保險署資料，截至目前為止，特約醫事服務機構違規次數累積達13722次。在所有重大違規事件中，大部分是詐欺行為。 健保審查機制主要以電腦隨機抽樣，再由人工進行調查。然而，這樣的審查方式無法有效抽取到違規醫事機構之樣本，造成審查效果不彰。 Benford’s Law又稱第一位數法則，其概念為第一位數的值越小則該數字出現的頻率越大，反之相反。該方法被應用於會計、金融、審計及經濟領域中。楊喻翔(2012)將Benford’s Law相關指標應用於我國全民健保上，並結合機器學習演算法來進行健保異常偵測。 Zaharia et al. (2012)提出了一種具容錯的群集記憶內運算模式 Apache Spark，在相同的運算節點及資源下，其資料運算效率及速度可勝出Hadoop MapReduce 20倍以上。 為解決健保異常查核效果不彰問題，本研究將採用Benford’s Law，使用國家衛生研究院發行之健保資料計算成為Benford’s Law指標和實務指標，接著並使用支援向量機和邏輯斯迴歸來建構出異常查核模型。然而健保資料量龐大，為加快運算時間，本研究使用Apache Spark做為運算環境，並以Hadoop MapReduce作為標竿，比較運算效率。 研究結果顯示，本研究撰寫的Spark程式運算時間能較MapReduce快2倍；在分類模型上，支援向量機和邏輯斯迴歸所進行的住院資料測試，敏感度皆有80%以上；而所進行的門診資料測試，兩個模型的準確率沒有住院資料高，但邏輯斯迴歸測試結果仍保有一定的準確性，在敏感度仍有75%，整體正確率有73%。 本研究使用Apache Spark節省處理大量健保資料的運算時間。其次本研究建立的智慧型異常查核模型，確實能查核出違約的醫事機構，而模型所查核出可能有詐欺及濫用健保之醫事機構，可進行下階段人工調查，最終得改善健保查核效力。 / Financial condition of National Health Insurance (NHI) has been wretched in recent years. The income statement in 2009 indicated that National Health Insurance Administration (NHIA) was in debt for NTD $58.2 billion. According to NHIA data, certain medical institutions in Taiwan violated the NHI laws for 13722 times. Among all illegal cases, fraud is the most serious. In order to find illegal medical institutions, NHIA conducted random sampling by computer. Once the data was collected, NHIA investigators got involved in the review process. However, the way to get the samples mentioned above cannot reveal the reality. Benford's law is called the First-Digit Law. The concept of Benford’s Law is that the smaller digits would appear more frequently, while larger digits would occur less frequently. Benford’s Law is applied to accounting, finance, auditing and economics. Yang(2012) used Benford’s Law in NHI data and he also used machine learning algorithms to do fraud detection. Zaharia et al. (2012) proposed a fault-tolerant in-memory cluster computing -Apache Spark. Under the same computing nodes and resources, Apache Spark’s computing is faster than Hadoop MapReduce 20 times. In order to solve the problem of medical claims review, Benford’s Law was applied to this study. This study used NHI data which was published by National Health Research Institutes. Then, we computed NHI data to generate Benford’s Law variables and technical variables. Finally, we used support vector machine and logistics regression to construct the illegal check model. During system development, we found that the data size was big. With the purpose of reducing the computing time, we used Apache Spark to build computing environment. Furthermore, we adopted Hadoop MapReduce as benchmark to compare the performance of computing time. This study indicated that Apache Spark is faster twice than Hadoop MapReduce. In illegal check model, with support vector machine and logistics regression, we had 80% sensitivity in inpatient data. In outpatient data, the accuracy of support vector machine and logistics regression were lower than inpatient data. In this case, logistics regression still had 75% sensitivity and 73% accuracy. This study used Apache Spark to compute NHI data with lower computing time. Second, we constructed the intelligent illegal check model which can find the illegal medical institutions for manual check. With the use of illegal check model, the procedure of medical claims review will be improved.

近二十年來，許多國內外規模大型的上市櫃公司因經濟情況的不穩定受到極大的影響，但為了使帳務好看，所以利用窗飾計巧使得報表美化。導致後續有許多財務報導重編、盈餘虛增等負面消息接連發生。這些訊息使得市場投資者感到不安，且不僅打亂原本資本市場的秩序，也使得社會大眾對整體市場的信任也相對減少，導致投資行為受到改變。過去文獻曾指出班佛法則可用來偵測財務報表數據是否盈餘管理，本研究的目的運用班佛法則針對台灣上市櫃公司之財務比率找出特徵數字，這些特徵數字是否可以偵測財報可能有誤。研究結果發現管理當局偏好於操弄淨利和 EPS 等與盈餘性值相關的會計項目；在損益表中，營業收入相關比率有高估的現象，費用類的有低估的現象；而的確形成紅旗警訊的特徵數字可以用來偵測財報有誤。 / In the last 20 years ago, many public company had larger capital were affected by the economic instability. They wanted to keep the reports in good-looking; thus, they use some skill like window dressing to achieve their purpose. This worst news like many financial reports needed to restate or inflated earnings communicate to public investors, and lead to investors feel anxious. These things result in the original market fall into disorder. General public loss their mind to believe the market and change their investment behavior. In the past, the former research found that they use the Benford’s Law to detect whether the financial reports have earnings management. The purpose of this study was to investigate whether the feature figure obtained from using Benford’s Law to measure the financial ratios from public company in Taiwan can detect the misstatement. The result is the managers prefer manipulate the account which has surplus nature like the net income and earnings-per-share. In the income statement, you will note the ratios are relative to income or earnings will be overestimate; on the other hand, the ratios are relative to cost or loss will be underestimate. And the flag made from the feature figure can detect whether the financial report have the misstatement.

“Some numbers really are more popular than others.” Mark J. Nigrini (1998a:15) The above idea appears to defy common sense. In a random sequence of numbers drawn from a company’s financial books, every digit from 1 to 9 seems to have a one-in-nine chance of being the leading digit when used in a series of numbers. But, according to a mathematical formula of over 60 years old making its way into the field of accounting, certain numbers are actually more popular than others (Nigrini, 1998a:15). Accounting numbers usually follow a mathematical law, named Benford’s Law, of which the result is so unpredictable that fraudsters and manipulators, as a rule, do not succeed in observing the Law. With this knowledge, the forensic accountant is empowered to detect irregularities, anomalies, errors or fraud that may be present in a financial data set. The main objective of this study was to evaluate the effectiveness of Benford’s Law as a tool for forensic accountants. The empirical research used data from Company X to test the hypothesis that, in the context of financial fraud investigations, a significant difference between the actual and expected frequencies of Benford’s Law could be an indication of an error, fraud or irregularity. The effectiveness of Benford’s Law was evaluated according to findings from the literature review and empirical study. The results indicated that a Benford’s Law analysis was efficient in identifying the target groups in the data set that needed further investigation as their numbers did not match Benford’s Law. / MCom (Forensic Accountancy), North-West University, Potchefstroom Campus, 2014

“Some numbers really are more popular than others.” Mark J. Nigrini (1998a:15) The above idea appears to defy common sense. In a random sequence of numbers drawn from a company’s financial books, every digit from 1 to 9 seems to have a one-in-nine chance of being the leading digit when used in a series of numbers. But, according to a mathematical formula of over 60 years old making its way into the field of accounting, certain numbers are actually more popular than others (Nigrini, 1998a:15). Accounting numbers usually follow a mathematical law, named Benford’s Law, of which the result is so unpredictable that fraudsters and manipulators, as a rule, do not succeed in observing the Law. With this knowledge, the forensic accountant is empowered to detect irregularities, anomalies, errors or fraud that may be present in a financial data set. The main objective of this study was to evaluate the effectiveness of Benford’s Law as a tool for forensic accountants. The empirical research used data from Company X to test the hypothesis that, in the context of financial fraud investigations, a significant difference between the actual and expected frequencies of Benford’s Law could be an indication of an error, fraud or irregularity. The effectiveness of Benford’s Law was evaluated according to findings from the literature review and empirical study. The results indicated that a Benford’s Law analysis was efficient in identifying the target groups in the data set that needed further investigation as their numbers did not match Benford’s Law. / MCom (Forensic Accountancy), North-West University, Potchefstroom Campus, 2014

Submitted by JOSIANE SANTOS DE OLIVEIRA (josianeso) on 2017-05-19T12:43:37Z No. of bitstreams: 1 Davenilcio Luiz de. Souza_.pdf: 539499 bytes, checksum: cf86851f0b7523f3b7d78589539fdbcb (MD5) / Made available in DSpace on 2017-05-19T12:43:37Z (GMT). No. of bitstreams: 1 Davenilcio Luiz de. Souza_.pdf: 539499 bytes, checksum: cf86851f0b7523f3b7d78589539fdbcb (MD5) Previous issue date: 2017-03-13 / Nenhuma / Os crimes de lavagem de dinheiro têm provocado grandes perdas aos países e a seus sistemas financeiros, o volume de dados em transações digitais representa dificuldade para a detecção deste tipo de ilícito. As auditorias em dados financeiros mostram-se limitadas na identificação de fraudes, pois em grande parte, ainda são realizadas com dados coletados por amostragem e incapazes de identificar as situações de delito em tempo real. Este trabalho, visando auxiliar no atendimento a esta lacuna, tem por objetivo propor um método estatístico de monitoramento por Cartas de Controle multivariadas, com base na Lei de Benford, para a detecção de suspeitas de fraude em lançamentos financeiros, entre eles os devidos à lavagem de dinheiro. Foi definido um modelo conceitual com distribuição de probabilidades representando dados oriundos de lançamentos financeiros, e adotada a suposição de que aderem a distribuição da Lei de Benford. Posteriormente foi considerada a distribuição empírica, estimada a partir dos próprios dados e dois procedimentos foram testados para verificar as suspeitas de fraude por lavagem de dinheiro utilizando a avaliação dos primeiros dígitos significativos: A Carta de Controle multivariada _2 e a Carta de Controle multivariada T2 de Hotelling. Foram simulados dados com auxílio do software R-Project até a ocorrência do 50.000o sinal. Foram avaliados casos simulados e reais, com o fim de exemplificar a operação do método. A partir da simulação, as duas Cartas de Controle testadas foram avaliadas quanto ao ARL, isto é, o número médio de observações até sinalizar que a série passou a operar em um estado fora de controle, o que significa a suspeita de lançamentos fraudulentos. Após aplicação do método de análise retrospectiva, com base nas proporções dos primeiros dígitos de Benford em lançamentos financeiros da campanha para Prefeito em 2016, não foram evidenciadas suspeitas de fraude nos dados obtidos junto ao sítio do Tribunal Superior Eleitoral (TSE). Em um conjunto de dados de uma instituição financeira, foram observados sinais de divergência entre as frequências dos primeiros dígitos nos lançamentos e nos valores esperados, porém os pontos além dos limites de controleidentificados encontram-se em um período próximo nas três análises realizadas, concentrando os dados de investigação para a auditoria financeira. A contribuição acadêmica deu-se pelo desenvolvimento de um modelo de aplicação de Cartas de Controle multivariadas e da Lei de Benford, com uma abordagem inovadora do controle estatístico de processos voltado à área financeira, utilizando recurso computacional acessível, de fácil processamento, confiável e preciso, que permite aprimoramento por novas abordagens acadêmicas. No que tange à contribuição à sociedade, se dá pelo uso do modelo por entidades que atuam com movimentações financeiras e pela comunidade, em dados de organizações civis e estatais divulgados nos canais de informação, de modo a proporcionar a prática cidadã pelo acesso à análise e a constatação da idoneidade dos fatos e dos dados. / Large losses are generated in the countryes financial systems, by money laundering. The volume of financial data is big issue to identify digital crime and money laundering. Audits in financial data have limitations in detecting fraud, in large part it is still performed in a traditional way, data are collected by sampling and often unable to identify a real-time crime situation. This research is aiming to serve in addressing this gap, to propose an monitoring statistical method, from multivariate control chart based on Benford’s law for detecting suspicious of fraud in financial data, including those due to money laundering. It was initially defined as a conceptual model in order to determine the type of probability distribution that represents data from financial launches. It was adopted an assumption that this type of data adheres to the Benford’s Law distribution. Subsequently, an empirical distribution was obtained, estimated from the own data. Two procedures were tested to verify a suspected money laundering fraud through the significant first-digit assessment: The Multivariate 2 Control Chart and the Multivariate Hotelling’s T2 Control Chart. Data were simulated using the R-Project software until the occurrence of the 50.000o signal. Finally, the simulation procedures were applied to real data in order to exemplify the method operationally. From the simulation, the two Control Charts tested were evaluated for ARL, that is, average number of observations until the signaling that the series started to operate in an out-of-control state, which it means suspicious of fraudulent launches. The application of the retrospective analysis method in the financial launchings of county’s campaign from 2016 Elections in five capitals of Brazil, based on the expected proportions from the first digit given by Benford’s Law, no suspicions fraud were evidenced in the data obtained from the site of Tribunal Superior Eleitoral (TSE). Considering the application in a set of data from a financial institution, signs of divergence between the frequencies of the first digits of the entries and the expected values were observed, but these points beyond the identified limits are close in all three analyzes. Indicating the period of the data which ones the audit will focus in a further investigation. Academic contribution is identified by developing a multivariate Control Chart together the Benford’s law in an application model with an innovative approach to the statistical process control aimed at the financial area,using accessible, easy to process, reliable and accurate computational resources that allow improvement through new academic approaches. As regard to the contribution to society, it is given the opportunity of applying the model by financial entities and the community in the data of civil and state organizations, disclosed in the information channels in order to provide access to analysis and verification of the suitability of facts and data by citizen practice.