A rank-size approach to the analysis of socio-economics data

This PhD thesis deals with a deep exploration of two key natural and human facts. The first one is related to the earthquakes, while the second one is associated to the content of the official speeches of the US Presidents. In particular, our aim is to define the extent of the economic damages deriving from earthquakes based on a large series of magnitudes over a rather large period. On the other hand, we investigate the economic impact of the speeches of the US Presidents on the financial market, with a specific reference to the Standard and Poor's 500. Our main objective is to give a contribution into the economic policy field by taking into consideration these phenomena from a different and innovative perspective. We employ several methodological tools. However, we can identify the ground of the analysis with the econophysic instruments related to the rank-size law. It is a set of different functions applied with the aim of exploring the properties of large sets of data, even when they are distributed over time and error bars are not clear because of peculiar sampling conditions. In the chapter of this thesis that concern the earthquakes as well as those referring to the speeches of the USA presidents, we show and comment the results of the Levenberg-Marquardt Non-linear Least-Squares Algorithm used to fit different rank-size laws. The resulting estimations are used for grasping relevant economics conclusion from different perspective. Anyway, the main findings are obtained thanks to the ability of rank-size laws of giving information about economics and social events by the means of proper manipulations of the functions parameters. For the study of the US Presidents’ speeches, as a side scientific product, we also analyze the distances between the series of frequencies of the economic terms present into the US Presidents speeches and the Standard & Poor's 500 index. At this aim, we adopt a probabilistic approach but also a mere topological perspective. In fact, entropy measures and several concepts of vectoral distances are compared.