This diploma thesis is focused on determining the degree of presence of Benford's law in citation data. The data and their acquisition are described in detail. The most extensive analysis was performed on a dataset of 8.6 million records of scientific outputs from the Web of Science database, over a five-year period, with a selection of the three most numerous and most cited types of documents. Descriptive MAD (Mean Absolute Deviation) statistic were used to determine the degree of presence of Benford's law. The degree of presence of Benford's law was also determined for two datasets, the production of public universities in the Czech Republic and the Academy of Sciences of the Czech Republic under the same conditions as in other analyses.

目前健保局所能查核到的違規案件來源有五項，即民眾檢舉、投保單位經辦人檢舉、審查費用時發現異常而移辦、專案稽查、繳回之健保卡發現異常。但只有審查費用流程應用電腦檔案分析可透過大量的資料分析方法篩選出異常院所。然而，電腦檔案分析只能偵測醫師的服務量是否「偏離常態分配」，亦即只能偵查出某些醫師或院所可能做了過多不必要的服務，而無法偵測出虛報或詐欺等行為。 因而，本研究透過大量詐欺文獻回顧，發現其中Bolton & Hand (2002)指出一個最佳的例子為應用Benford定律的數字分析。Benford定律即是凡符合此法則的資料中，其第一位數的值越小者則出現的頻率就越大，而數值越大者出現的機率就越小。近幾年，Benford定律被應用在不同領域的舞弊或詐欺的審查流程中。 由於目前尚未有專文探討運用Benford定律於臺灣健保醫療費用異常之相關研究。本研究以Benford定律為基礎，利用健保研究資料庫的1999至2003年住院全部及門診抽樣的申報資料進行實證，步驟上有三：一、進行全體住院及門診機構的整體實證，二、檢視單獨以數字分析法是否可以找出異常機構，三、提出一個智慧型費用異常偵測模型並實證其效果。 本研究結論有三： 一、健保特約機構中，住院機構的健保費申請數字符合第一位數的Benford定律，第二、第三及第四位位數不符合。而其中的一般費用部分符合第一、二、三、四位數的Benford定律，論病計酬案件則只有第一位數符合。至於健保費的申請數字之第二、第三及第四位數不符全之原因為論病計酬案件不符合Benford定律，此乃因為論病計酬案件之特殊計價方式所造成。 二、本研究指出單獨應用Benford定律的數字分析方法檢驗的確能找出異常院所，但同時也容易將正常院所誤判為異常，在利用卡方檢定、Cramer’s V統計值判斷法，無論是住院或門診機構，由於鑑別度不高造成整體正確率不佳，由此可推論單純利用數字分析法不足以檢驗出異常院所，因此需要再進一步結合其他工具。 三、本研究所建構的智慧型費用異常偵測模型，是以GHSOM類神經網路進行變數選取工作，找出數個變數群組後，分別利用RBFNN(徑向基類神經網路)、GRNN（通用迴歸類神經網路）及ERNN（Elman反饋式類神經網路）等進行異常院所預判，並以逐步邏輯斯迴歸模型作為Benchmark，結果是以逐步邏輯斯迴歸模型所構建的線性模型得到比較好的效果，本研究推論原因可能為應用Benford定律的衍生指標和異常/正常院所之間就存在線性關係，因此可以利用邏輯斯迴歸模型來預判，並利用類神經網路模型加以佐證之。 因此，本研究希望利用Benford定律的計算智慧技術能運用於健保資料庫，進行大規模電腦初步審查，找出更多不良醫療院所之異常申報之來源，以提供實地查核進而查到真正違規之醫療院所，如此可遏止醫療院所之犯意，進而節省健保支出，健全其財務收支平衡，為健保永續經營貢獻一份心力。 / There are five sources of illegal medical cases checked by BNHI (Bureau of National Health Insurance): reported by public, reported by the operator of insured unit, unusual findings while auditing expenses, special case audit, and unusual findings for returned health insurance cards. The abnormal medical institutions can only be found out by analyzing digital data in the source of auditing expenses. However, the digital data can only detect whether the physicians’ service deviates from the normal distribution (excessive unnecessary service offered by some physicians or hospitals), instead of the false claim of medical expenses and fraud behavior. Thus, by reviewing a lot of fraud literature, this study finds the best example in Bolton & Hand (2002) is digit analysis of Benford's Law. Benford's Law points that the smaller the first digit is, the more frequent the digit shows, vice versa. In recent years, Benford's law has been applied in fraud review process in different fields. So far no specific article has applied Benford's Law in the research related to the BNHI medical expenses, so we did a study using inpatient (total) and outpatient (sampling) data from 1999 to 2003. There are three steps in this study: 1. Overall empirical study of all inpatient and outpatient medical institutions. 2. Try to find out the unusual medical institutions only using digit analysis. 3. Find out a smart anomaly detection model and verify its effectiveness. There are three conclusions of the study: 1. For the health insurance expenses applied by the BNHI-contracted inpatient institutions, the frequency of the first digit accords with Benford's Law, while the second, third, and fourth digits does not accord with Benford's Law. For the general health insurance expense, the frequencies of the first, second, third, and fourth digit accord with Benford's Law. While only the first digit meets Benford's Law for cases paid by disease, as its special pricing method causes the different frequencies of the second, third, and fourth digits of health insurance expenses. 2. This study shows that the digit analysis of Benford's Law does contribute to find out the abnormal institutions, but also pay the price of misidentify the normal institutions. By using chi-square test and Cramer's V statistics method, the low discrimination rates of both inpatient and outpatient hospitals leads to poor overall accuracy. It suggests that the simple method of digit analysis is insufficient to test the abnormal institutes, and further investigation with other tools is requested. 3. This study establishes a smart anomaly detection model of health insurance expense, which is based on variable selection with GHSOM neural networks to identify the optimal model, and then uses RBFNN (radial basis function neural network), GRNN (general regression neural network), and ERNN (Elman recurrent neural network) to predict the abnormal institutions. Comparing RBFNN, GRNN and ERNN with the stepwise logistic regression model as the Benchmark, the study concludes that the linear relationship between derived indicator of Benford's Law and abnormal/normal institutions exits. Therefore, we can predict by logistic regression model and verify by neural network model. The study intends to apply the smart technology of Benford's Law to the large-scale preliminary review of the National Health Insurance database, which can help to identify the sources of the anomaly expenses of medical institutions and find out the fraud ones. Therefore, the decreasing fraud of medical institutions will cut down the health insurance expense for financial break-even. We hope we can contribute to the sustainable development of health insurance.。

This diploma thesis is focused on a role of reference interest rates in developed market economies. There are described interest rate transmission mechanism and discussed factors, which led to manipulation of the LIBOR. How the manipulation was done and what reactions of supervisory authorities it induced. There are also listed proposed recommendations to ensure transparent reference indicators. This work also includes analysis of reference interest rates used in the Czech Republic. At the end of the thesis can be found application of a reference rate fixing process in a game theory model as well as application of Benford´s law as an indicator of the manipulation.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-02-21T15:12:08Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_JoséVianneyMendonçaDeAlencastroJr.pdf: 648691 bytes, checksum: f2fbc98e547f0284f5aef34aee9249ca (MD5) / Made available in DSpace on 2017-02-21T15:12:08Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_JoséVianneyMendonçaDeAlencastroJr.pdf: 648691 bytes, checksum: f2fbc98e547f0284f5aef34aee9249ca (MD5) Previous issue date: 2016-09-09 / A lei de Newcomb-Benford, também conhecida como a lei do dígito mais significativo, foi descrita pela primeira vez por Simon Newcomb, sendo apenas embasada estatisticamente após 57 anos pelo físico Frank Benford. Essa lei rege grandezas naturalmente aleatórias e tem sido utilizada por várias áreas como forma de selecionar e validar diversos tipos de dados. Em nosso trabalho tivemos como primeiro objetivo propor o uso de um método substituto ao qui-quadrado, sendo este atualmente o método comumente utilizado pela literatura para verificação da conformidade da Lei de Newcomb-Benford. Fizemos isso pois em uma massa de dados com uma grande quantidade de amostras o método qui-quadrado tende a sofrer de um problema estatístico conhecido por excesso de poder, gerando assim resultados do tipo falso negativo na estatística. Dessa forma propomos a substituição do método qui-quadrado pelo método de Kolmogorov-Smirnov baseado na Função de Distribuição Empírica para análise da conformidade global, pois esse método é mais robusto não sofrendo do excesso de poder e também é mais fiel à definição formal da Lei de Benford, já que o mesmo trabalha considerando as mantissas ao invés de apenas considerar dígitos isolados. Também propomos investigar um intervalo de confiança para o Kolmogorov-Smirnov baseando-nos em um qui-quadrado que não sofre de excesso de poder por se utilizar o Bootstraping. Em dois artigos publicados recentemente, dados de exoplanetas foram analisados e algumas grandezas foram declaradas como conformes à Lei de Benford. Com base nisso eles sugerem que o conhecimento dessa conformidade possa ser usado para uma análise na lista de objetos candidatos, o que poderá ajudar no futuro na identificação de novos exoplanetas nesta lista. Sendo assim, um outro objetivo de nosso trabalho foi explorar diversos bancos e catálogos de dados astronômicos em busca de grandezas, cuja a conformidade à lei do dígito significativo ainda não seja conhecida a fim de propor aplicações práticas para a área das ciências astronômicas. / The Newcomb-Benford law, also known as the most significant digit law, was described for the first time by astronomer and mathematician Simon Newcomb. This law was just statistically grounded after 57 years after the Newcomb’s discovery. This law governing naturally random greatness and, has been used by many knowledge areas to validate several kind of data. In this work, the first goal is propose a substitute of qui-square method. The qui-square method is the currently method used in the literature to verify the Newcomb-Benford Law’s conformity. It’s necessary because in a greatness with a big quantity of samples, the qui-square method can has false negatives results. This problem is named Excess of Power. Because that, we proposed to use the Kolmogorov-Smirnov method based in Empirical Distribution Function (EDF) to global conformity analysis. Because this method is more robust and not suffering of the Excess of Power problem. The Kolmogorov-Smirnov method also more faithful to the formal definition of Benford’s Law since the method working considering the mantissas instead of single digits. We also propose to invetigate a confidence interval for the Kolmogorov-Smirnov method based on a qui-square with Bootstrapping strategy which doesn’t suffer of Excess of Power problem. Recently, two papers were published. I this papaers exoplanets data were analysed and some greatness were declared conform to a Newcomb-Benford distribution. Because that, the authors suggest that knowledge of this conformity can be used for help in future to indentify new exoplanets in the candidates list. Therefore, another goal of this work is explorer a several astronomicals catalogs and database looking for greatness which conformity of Benford’s law is not known yet. And after that , the authors suggested practical aplications for astronomical sciences area.

“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.

This thesis analyzes techniques of manipulation of accounting data for the purpose of fraud. It is further looking for methods, which could be capable of detecting these manipulations and it verifies the efficiency of the procedures already in use. A theoretical part studies method of financial analysis, statistical methods, Benford's tests, fuzzy matching and technologies of machine learning. Practical part verifies the methods of financial analysis, Benford's tests, algorithms for fuzzy matching and neural networks.