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Nesta dissertação aborda-se a aplicação de Leis de PotĂȘncia (LPs), tambĂ©m designadas de Leis de Pareto ou Leis de Zipf, a dados econĂłmicos. As LPs sĂŁo distribuiçÔes estatĂsticas amplamente usadas na compreensĂŁo de sistemas naturais e artificiais. O aparecimento das LPs deve-se a Vilfredo Pareto que, no sĂ©culo XIX, publicou o manual de economia polĂtica,âCours dâEconomie Politiqueâ. Nesse manual refere que grande parte da economia mundial segue uma LP, em que 20% da população reĂșne 80% da riqueza do paĂs. Esta propriedade carateriza uma variĂĄvel que segue uma distribuição de Pareto (ou LP). Desde entĂŁo, as LPs foram aplicadas a outros fenĂłmenos, nomeadamente a ocorrĂȘncia de palavras em textos, os sobrenomes das pessoas, a variação dos rendimentos pessoais ou de empresas, o nĂșmero de vĂtimas de inundaçÔes ou tremores de terra, os acessos a sĂtios da internet, etc.
Neste trabalho, Ă© estudado um conjunto de dados relativos Ă s fortunas particulares ou coletivas de pessoas ou organizaçÔes. Mais concretamente sĂŁo analisados dados recolhidos sobre as fortunas das mulheres mais ricas do mundo, dos homens mais ricos no ramo da tecnologia, das famĂlias mais ricas, das 20 mulheres mais ricas da AmĂ©rica, dos 400 homens mais ricos da AmĂ©rica, dos homens mais ricos do mundo, dos estabelecimentos mais ricos do mundo, das empresas mais ricas do mundo e dos paĂses mais ricos do mundo, bem como o valor de algumas empresas no mercado de açÔes. Os resultados obtidos revelam uma boa aproximação de parte desses dados a uma LP simples e uma boa aproximação pelos restantes dados a uma LP dupla. Observa-se, assim, diferenciação na forma de crescimento das fortunas nos diferentes casos estudados.
Como trabalho futuro, procurar-se-ĂĄ analisar estes e outros dados, utilizando outras distribuiçÔes estatĂsticas, como a exponencial ou a lognormal, que possuem comportamentos semelhantes Ă LP, com o intuito de serem comparados os resultados. Um outro aspeto interessante serĂĄ o de encontrar a explicação analĂtica para as vantagens da aproximação de dados econĂłmicos por uma LP simples vs por uma LP dupla.
In this study we consider Power Laws (PLs), also known as Pareto Laws or Zipf Laws. PLs are statistical distributions. Vilfredo Pareto, in the XIX century, was a pioneer in the study of PLs. He states, in his manual of political economy, "Cours d'Economie Politique", that a large part of the world economy follows a particular distribution, in which 20% of the population gathers 80% of the total wealth, and so, a small fraction of the society controls the largest share of the money. This summarizes the behavior of a variable that follows a Pareto distribution (or, PL). Until now, several researchers applied PLs to other natural and human-made phenomena, such as the occurrence of words in texts, personâs surnames, the variation in personal incomes or businesses, the number of casualties in floods and earthquakes, on the internet, amongst others. This work focuses on the application of PLs to economic data from private persons and organizations. More specifically, it is studied data concerning fortunes of the richest women in the world, of the richest men in any branch of technology, of the richest families, of the 20 richest women of America, of the 400 richest men in America, the world's richest men, the world's richest companies, the companiesâ values at stock market. The results obtained reveal a good approximation of certain data by a single PL and the remaining data is better approximated by a double PL. There is, thus, differentiation in the form of growth of fortunes in the different cases studied. As future work, we will analyze these and other data, using other statistical distributions, such as exponential or lognormal, that have similar behaviors to the PL, with the intent to compare the outcomes. Another interesting aspect will be to find the analytic explanation of the benefits of economic data approximation by a simple LP vs for a double LP.
In this study we consider Power Laws (PLs), also known as Pareto Laws or Zipf Laws. PLs are statistical distributions. Vilfredo Pareto, in the XIX century, was a pioneer in the study of PLs. He states, in his manual of political economy, "Cours d'Economie Politique", that a large part of the world economy follows a particular distribution, in which 20% of the population gathers 80% of the total wealth, and so, a small fraction of the society controls the largest share of the money. This summarizes the behavior of a variable that follows a Pareto distribution (or, PL). Until now, several researchers applied PLs to other natural and human-made phenomena, such as the occurrence of words in texts, personâs surnames, the variation in personal incomes or businesses, the number of casualties in floods and earthquakes, on the internet, amongst others. This work focuses on the application of PLs to economic data from private persons and organizations. More specifically, it is studied data concerning fortunes of the richest women in the world, of the richest men in any branch of technology, of the richest families, of the 20 richest women of America, of the 400 richest men in America, the world's richest men, the world's richest companies, the companiesâ values at stock market. The results obtained reveal a good approximation of certain data by a single PL and the remaining data is better approximated by a double PL. There is, thus, differentiation in the form of growth of fortunes in the different cases studied. As future work, we will analyze these and other data, using other statistical distributions, such as exponential or lognormal, that have similar behaviors to the PL, with the intent to compare the outcomes. Another interesting aspect will be to find the analytic explanation of the benefits of economic data approximation by a simple LP vs for a double LP.
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Keywords
Leis de PotĂȘncia (LP) Lei de Pareto Lei de Zipf Dados econĂłmicos LP simples LP dupla Power Laws (PL) Pareto Laws Zipf Law Economic data Single PL Double PL