Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Estimating extreme value cumulative distribution functions using bias-corrected kernel approaches

We propose a new kernel estimation of the cumulative distribution function based on transformation and on bias reducing techniques. We derive the optimal bandwidth that minimises the asymptotic integrated mean squared error. The simulation results show that our proposed kernel estimation improves alternative approaches when the variable has an extreme value distribution with heavy tail and the sample size is small.

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Dry months in the agricultural region of Ribeirão Preto, state of São Paulo-Brazil: an study based on the extreme value theory

The application of the Extreme Value Theory (EVT) to model the probability of occurrence of extreme low Standardized Precipitation Index (SPI) values leads to an increase of the knowledge related to the occurrence of extreme dry months. This sort of analysis can be carried out by means of two approaches: the block maxima (BM; associated with the General Extreme Value distribution) and the peaks-over-threshold (POT; associated with the Generalized Pareto distribution). Each of these procedures has its own advantages and drawbacks. Thus, the main goal of this study is to compare the performance of BM and POT in characterizing the probability of occurrence of extreme dry SPI values obtained from the weather station of Ribeirão Preto-SP (1937-2012). According to the goodness-of-fit tests, both BM and POT can be used to assess the probability of occurrence of the aforementioned extreme dry SPI monthly values. However, the scalar measures of accuracy and the return level plots indicate that POT provides the best fit distribution. The study also indicated that the uncertainties in the parameters estimates of a probabilistic model should be taken into account when the probability associated with a severe/extreme dry event is under analysis.

Empirical global value chain analysis in electronics and automobile industries :An application of Asian international input-output tables

This study aims to examine the international value distribution structure among major East Asian economies and the US. The mainstream trade theory explains the gains from trade; however, global value chain (GVC) approach emphasises uneven benefits of globalization among trading partners. The present study is mainly based on this view, examining which economy gains the most and which the least from the East Asian production networks. Two key industries, i.e., electronics and automobile, are our principle focus. Input-output method is employed to trace the creation and flows of value-added within the region. A striking fact is that some ASEAN economies increasingly reduce their shares of value-added, taken by developed countries, particularly by Japan. Policy implications are discussed in the final section.

Trimmed Likelihood Estimation of the Parameters of the Generalized Extreme Value Distributions: a Monte-Carlo Study

2000 Mathematics Subject Classification: Primary 62F35; Secondary 62P99

The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis

Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intensity of their extremes. Therefore, the assumption of stationarity is violated and alternative methods to conventional stationary extreme value analysis (EVA) must be adopted. Using the example of environmental variables subject to climate change, in this study we introduce the transformed-stationary (TS) methodology for non-stationary EVA. This approach consists of (i) transforming a non-stationary time series into a stationary one, to which the stationary EVA theory can be applied, and (ii) reverse transforming the result into a non-stationary extreme value distribution. As a transformation, we propose and discuss a simple time-varying normalization of the signal and show that it enables a comprehensive formulation of non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with a constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the results from (a) a stationary EVA on quasi-stationary slices of non-stationary series and (b) the established method for non-stationary EVA. However, the proposed technique comes with advantages in both cases. For example, in contrast to (a), the proposed technique uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels. Furthermore, with respect to (b), it decouples the detection of non-stationary patterns from the fitting of the extreme value distribution. As a result, the steps of the analysis are simplified and intermediate diagnostics are possible. In particular, the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on the running mean and the standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and is easy to implement and control. An open-source MAT-LAB toolbox has been developed to cover this methodology, which is available at https://github.com/menta78/tsEva/(Mentaschi et al., 2016).

Dependence of IVIM-DWI estimations on acquisition parameters

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Inundações urbanas: desafios ao ordenamento do território. O caso da Cidade da Praia (Cabo Verde)

Pela sua posição geográfica e particulares condições climáticas, devidas à sua inserção na faixa saheliana com caraterísticas de marcada aridez, Cabo Verde é um arquipélago com condições naturais adversas, pautado principalmente pela seca prolongada. Muitas vezes esta conjuntura é interpolada por curtos períodos de fortes chuvadas que podem originar cheias e inundações nos principais centros urbanos. Os eventos ocorridos revelam consequências graves, desde prejuízos na agricultura, perda de animais, destruição de infra-estruturas, perda de bens materiais e, mesmo, vítimas humanas mortais. Este estudo tem como objetivos principais: (i) perceber os problemas e desafios que se colocam à cidade da Praia (maior centro urbano do país, com forte crescimento e expansão urbana) perante situações de inundação; (ii) contribuir para o maior conhecimento das causas e consequências dessas inundações; (iii) definir quais as áreas de maior suscetibilidade às cheias e quais as que possuem um maior risco potencial. Optou-se por uma metodologia integrada, através do levantamento bibliográfico, cartográfico, numérico e percetivo (com base em entrevistas e inquéritos). Para o estudo das bacias hidrográficas foram calculados índices morfométricos, definidas classes de permeabilidade do substrato geológico e aplicado o método multicritério de Reis (2011) para a definição das áreas suscetíveis às cheias. Analisaram-se as precipitações máximas diárias anuais e respetivos períodos de retorno, com a aplicação do método de Gumbel. A análise de notícias de jornais, referentes ao período compreendido entre 1980 e 2011, foi fundamental para o conhecimento da distribuição espácio-temporal dos eventos perigosos de inundação em Cabo Verde e na cidade da Praia. Os resultados obtidos revelam um significativo grau de suscetibilidade às cheias na cidade da Praia. As áreas de maior risco potencial às inundações encontram-se no setor central da cidade, resultante da conjugação da convergência do escoamento das três ribeiras principais, da elevada densidade populacional e de construção desordenada nos leitos de cheia e nas áreas deprimidas, onde se acumulam as águas.

Inundações Urbanas - Desafios ao Ordenamento do Território - O

Pela sua posição geográfica e particulares condições climáticas, devidas à sua inserção na faixa saheliana com caraterísticas de marcada aridez, Cabo Verde é um arquipélago com condições naturais adversas, pautado principalmente pela seca prolongada. Muitas vezes esta conjuntura é interpolada por curtos períodos de fortes chuvadas que podem originar cheias e inundações nos principais centros urbanos. Os eventos ocorridos revelam consequências graves, desde prejuízos na agricultura, perda de animais, destruição de infra-estruturas, perda de bens materiais e, mesmo, vítimas humanas mortais. Este estudo tem como objetivos principais: (i) perceber os problemas e desafios que se colocam à cidade da Praia (maior centro urbano do país, com forte crescimento e expansão urbana) perante situações de inundação; (ii) contribuir para o maior conhecimento das causas e consequências dessas inundações; (iii) definir quais as áreas de maior suscetibilidade às cheias e quais as que possuem um maior risco potencial. Optou-se por uma metodologia integrada, através do levantamento bibliográfico, cartográfico, numérico e percetivo (com base em entrevistas e inquéritos). Para o estudo das bacias hidrográficas foram calculados índices morfométricos, definidas classes de permeabilidade do substrato geológico e aplicado o método multicritério de Reis (2011) para a definição das áreas suscetíveis às cheias. Analisaram-se as precipitações máximas diárias anuais e respetivos períodos de retorno, com a aplicação do método de Gumbel. A análise de notícias de jornais, referentes ao período compreendido entre 1980 e 2011, foi fundamental para o conhecimento da distribuição espácio-temporal dos eventos perigosos de inundação em Cabo Verde e na cidade da Praia. Os resultados obtidos revelam um significativo grau de suscetibilidade às cheias na cidade da Praia. As áreas de maior risco potencial às inundações encontram-se no setor central da cidade, resultante da conjugação da convergência do escoamento das três ribeiras principais, da elevada densidade populacional e de construção desordenada nos leitos de cheia e nas áreas deprimidas, onde se acumulam as águas.

Characteristics of 2D convective structures in Catalonia (NE Spain): an analysis using radar data and GIS

Flood simulation studies use spatial-temporal rainfall data input into distributed hydrological models. A correct description of rainfall in space and in time contributes to improvements on hydrological modelling and design. This work is focused on the analysis of 2-D convective structures (rain cells), whose contribution is especially significant in most flood events. The objective of this paper is to provide statistical descriptors and distribution functions for convective structure characteristics of precipitation systems producing floods in Catalonia (NE Spain). To achieve this purpose heavy rainfall events recorded between 1996 and 2000 have been analysed. By means of weather radar, and applying 2-D radar algorithms a distinction between convective and stratiform precipitation is made. These data are introduced and analyzed with a GIS. In a first step different groups of connected pixels with convective precipitation are identified. Only convective structures with an area greater than 32 km2 are selected. Then, geometric characteristics (area, perimeter, orientation and dimensions of the ellipse), and rainfall statistics (maximum, mean, minimum, range, standard deviation, and sum) of these structures are obtained and stored in a database. Finally, descriptive statistics for selected characteristics are calculated and statistical distributions are fitted to the observed frequency distributions. Statistical analyses reveal that the Generalized Pareto distribution for the area and the Generalized Extreme Value distribution for the perimeter, dimensions, orientation and mean areal precipitation are the statistical distributions that best fit the observed ones of these parameters. The statistical descriptors and the probability distribution functions obtained are of direct use as an input in spatial rainfall generators.

Innovaation luoman arvon jakautuminen arvoverkostossa

Innovaation kaupallinen menestys ei läheskään aina tuota samassa suhteessa menestystä kyseisen innovaation kehittäjälle. Arvoverkostojen muuttuessa yhä monimutkaisemmiksi on entistä tärkeämpää kyetä tunnistamaan innovaation hyötyjen jakautumisen logiikka, jotta yritykset voivat maksimoida innovaatiosta saatavat hyödyt ja turvata oman asemansa kilpailutilanteessa. Ongelma on viime vuosikymmeninä korostunut, kun yritykset ovat keskittyneet ydintoimintoihinsa ja tuotteen tai palveluksen tuottamiseksi tarvittava yritysverkosto on laajentunut. Myös aineettoman omaisuuden rooli on kasvattanut merkitystään erityisesti teknologiateollisuudessa ja luonut uudentyyppisiä yrityksiä ja liiketoimintamalleja yritysverkostoon. Tämän työn takoituksena on tarkastella kirjallisuudessa tehtyä tutkimusta innovaation hyötyjen jakautumisesta arvoketjussa ja –verkossa. Työssä pyritään tunnistamaan mitkä asiat vaikuttavat innovaation hyötyjen jakautumiseen verkoston eri toimijoiden kesken. Työssä ei pureuduta yksittäistapauksiin vaan käsitellään asioita yleisellä tasolla. Tällä tavoin työ pyrkii kasvattamaan lukijan ymmärrystä arvoketjun ja –verkon sisäisestä dynamiikasta ja siihen vaikuttavista ilmiöistä. Työssä esitellään innovaatiomallit ja arvoketjun käsite lyhyesti sekä tunnistetaan toimialojen siirtyminen arvoketjumaisesta rakenteesta arvoverkkomaiseen. Innovaation hyötyjen jakautumista käsitellään innovaattorin ja arvoketjun alkupään näkökulmasta sekä innovaation loppukäyttäjän näkökulmasta. Johtopäätöksissä on kiteytetty kirjallisuudesta tunnistettu dynamiikka oivallisen analyysin avulla. Tuloksissa on myös todettu aihealueen tutkimuksen olevan arvoketjun näkökulmasta suhteellisen vähäistä lukuunottamatta yksittäisiä casetutkimuksia ja pohdittu hieman syitä siihen.

Climate trends in the municipality of Pelotas, state of Rio Grande do Sul, Brazil

ABSTRACTChanges in the frequency of occurrence of extreme weather events have been pointed out as a likely impact of global warming. In this context, this study aimed to detect climate change in series of extreme minimum and maximum air temperature of Pelotas, State of Rio Grande do Sul, (1896 - 2011) and its influence on the probability of occurrence of these variables. We used the general extreme value distribution (GEV) in its stationary and non-stationary forms. In the latter case, GEV parameters are variable over time. On the basis of goodness-of-fit tests and of the maximum likelihood method, the GEV model in which the location parameter increases over time presents the best fit of the daily minimum air temperature series. Such result describes a significant increase in the mean values of this variable, which indicates a potential reduction in the frequency of frosts. The daily maximum air temperature series is also described by a non-stationary model, whose location parameter decreases over time, and the scale parameter related to sample variance rises between the beginning and end of the series. This result indicates a drop in the mean of daily maximum air temperature values and increased dispersion of the sample data.

Modelling European winter wind storm losses in current and future climate

Severe wind storms are one of the major natural hazards in the extratropics and inflict substantial economic damages and even casualties. Insured storm-related losses depend on (i) the frequency, nature and dynamics of storms, (ii) the vulnerability of the values at risk, (iii) the geographical distribution of these values, and (iv) the particular conditions of the risk transfer. It is thus of great importance to assess the impact of climate change on future storm losses. To this end, the current study employs—to our knowledge for the first time—a coupled approach, using output from high-resolution regional climate model scenarios for the European sector to drive an operational insurance loss model. An ensemble of coupled climate-damage scenarios is used to provide an estimate of the inherent uncertainties. Output of two state-of-the-art global climate models (HadAM3, ECHAM5) is used for present (1961–1990) and future climates (2071–2100, SRES A2 scenario). These serve as boundary data for two nested regional climate models with a sophisticated gust parametrizations (CLM, CHRM). For validation and calibration purposes, an additional simulation is undertaken with the CHRM driven by the ERA40 reanalysis. The operational insurance model (Swiss Re) uses a European-wide damage function, an average vulnerability curve for all risk types, and contains the actual value distribution of a complete European market portfolio. The coupling between climate and damage models is based on daily maxima of 10 m gust winds, and the strategy adopted consists of three main steps: (i) development and application of a pragmatic selection criterion to retrieve significant storm events, (ii) generation of a probabilistic event set using a Monte-Carlo approach in the hazard module of the insurance model, and (iii) calibration of the simulated annual expected losses with a historic loss data base. The climate models considered agree regarding an increase in the intensity of extreme storms in a band across central Europe (stretching from southern UK and northern France to Denmark, northern Germany into eastern Europe). This effect increases with event strength, and rare storms show the largest climate change sensitivity, but are also beset with the largest uncertainties. Wind gusts decrease over northern Scandinavia and Southern Europe. Highest intra-ensemble variability is simulated for Ireland, the UK, the Mediterranean, and parts of Eastern Europe. The resulting changes on European-wide losses over the 110-year period are positive for all layers and all model runs considered and amount to 44% (annual expected loss), 23% (10 years loss), 50% (30 years loss), and 104% (100 years loss). There is a disproportionate increase in losses for rare high-impact events. The changes result from increases in both severity and frequency of wind gusts. Considerable geographical variability of the expected losses exists, with Denmark and Germany experiencing the largest loss increases (116% and 114%, respectively). All countries considered except for Ireland (−22%) experience some loss increases. Some ramifications of these results for the socio-economic sector are discussed, and future avenues for research are highlighted. The technique introduced in this study and its application to realistic market portfolios offer exciting prospects for future research on the impact of climate change that is relevant for policy makers, scientists and economists.