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We estimate Growth-at-Risk (GaR) statistics for the US economy using daily regressors. We show that the relative importance, in terms of forecasting power, of financial and real variables is time varying. Indeed, the optimal forecasting weights of these types of variables were clearly different during the Global Financial Crisis and the recent Covid-19 crisis, which reflects the dissimilar nature of the two crises. We introduce the LASSO and the Elastic Net into the family of mixed data sampling models used to estimate GaR and show that these methods outperform past candidates explored in the literature. The role of the VXO and ADS indicators was found to be very relevant, especially in out-of-sample exercises and during crisis episodes. Overall, our results show that daily information for both real and financial variables is key for producing accurate point and tail risk nowcasts and forecasts of economic activity.

Treballs Finals del Màster de Ciències Actuarials i Financeres, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2021-2022, Tutor: M. Mercè Claramunt Bielsa, The aim of this research is to study the implementation of segmentation in bonus-malus systems that base its analysis in the random variable number of claims. To this end, the theoretical framework proposed by Norberg for the construction of this a posteriori pricing method, for both not segmented and segmented case, is presented. This formulation has allowed the computation of the relative pure premiums and the premiums when unitary claim amount is assumed under different examples and scenarios. Then the different paths of premiums for certain insureds from simulated datasets are assessed. It is also evaluated this framework to surcharge premiums.

Multiple quantitative methods for single-case experimental design data have been applied to multiple-baseline, withdrawal, and reversal designs. The advanced data analytic techniques historically applied to single-case design data are primarily applicable to designs that involve clear sequential phases such as repeated measurement during baseline and treatment phases, but these techniques may not be valid for alternating treatment design (ATD) data where two or more treatments are rapidly alternated. Some recently proposed data analytic techniques applicable to ATD are reviewed. For ATDs with random assignment of condition ordering, the Edgington's randomization test is one type of inferential statistical technique that can complement descriptive data analytic techniques for comparing data paths and for assessing the consistency of effects across blocks in which different conditions are being compared. In addition, several recently developed graphical representations are presented, alongside the commonly used time series line graph. The quantitative and graphical data analytic techniques are illustrated with two previously published data sets. Apart from discussing the potential advantages provided by each of these data analytic techniques, barriers to applying them are reduced by disseminating open access software to quantify or graph data from ATDs. ispartof: Perspectives on Behavior Science vol:45 issue:1 pages:1-36 ispartof: location:Switzerland status: Published online

Treballs Finals del Màster de Ciències Actuarials i Financeres, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2020-2021, Tutor: Teresa Costa, Eva Boj, El presente trabajo busca desarrollar una aplicación con Shiny de RStudio para el cálculo estocástico de provisiones en seguros no vida que incluyen el efecto del año de calendario y obtener los resultados propuestos en los métodos deterministas de separación Aritmético (Verbeek, 1972) y Geométrico (Taylor, 1979), de forma que los inputs y outputs puedan ser visualizados a través de una interfaz gráfica interactiva. La metodología de cálculo hace uso del Modelo Lineal Generalizado y la técnica estadística de remuestreo o Bootstrapping propuesta por Björkwall et al. (2009, 2010) para la estimación de las reservas.

© 2021 by the authors., The prediction of spatial and temporal variation of soil water content brings numerous benefits in the studies of soil. However, it requires a considerable number of covariates to be included in the study, complicating the analysis. Integrated nested Laplace approximations (INLA) with stochastic partial differential equation (SPDE) methodology is a possible approach that allows the inclusion of covariates in an easy way. The current study has been conducted using INLA-SPDE to study soil moisture in the area of the Valencia Anchor Station (VAS), soil moisture validation site for the European Space Agency SMOS (Soil Moisture and Ocean Salinity). The data used were collected in a typical ecosystem of the semiarid Mediterranean conditions, subdivided into physio-hydrological units (SMOS units) which presents a certain degree of internal uniformity with respect to hydrological parameters and capture the spatial and temporal variation of soil moisture at the local fine scale. The paper advances the knowledge of the influence of hydrodynamic properties on VAS soil moisture (texture, porosity/bulk density and soil organic matter and land use). With the goal of understanding the factors that affect the variability of soil moisture in the SMOS pixel (50 km × 50 km), five states of soil moisture are proposed. We observed that the model with all covariates and spatial effect has the lowest DIC value. In addition, the correlation coefficient was close to 1 for the relationship between observed and predicted values. The methodology applied presents the possibility to analyze the significance of different covariates having spatial and temporal effects. This process is substantially faster and more effective than traditional kriging. The findings of this study demonstrate an advancement in that framework, demonstrating that it is faster than previous methodologies, provides significance of individual covariates, is reproducible, and is easy to compare with models.

Background The study assesses the prevalence rates of alcohol- and drug-involved driving in Catalonia (Spain). Method Drivers were randomly selected for roadside testing using a stratified random sampling procedure representative of all vehicles circulating on non-urban roads. Mandatory alcohol and drug tests were performed during autumn 2017. A sample of 6860 drivers were tested for alcohol use, of these 671 were also tested for drugs. Standard procedures were employed by traffic officers to detect alcohol and drug use. Alcohol breath tests were performed with breathalyser devices and on-site drug screening systems were used to test for drugs. Results The prevalence of alcohol use above the legal limit and drug use were 1.2 % (95 % CI: 0.9–1.5 %) and 8.3 % (95 % CI: 5.8–11.2 %), respectively. The most frequent drugs detected were THC (5.6 %, 95 % CI: 3.7–8.0 %), cocaine (3.5 %, 95 % CI: 2.0–5.5 %) and amphetamines (1.6 %, 95 % CI: 0.6–3.4 %). Alcohol use was detected more frequently on conventional roads, at weekends and during night-time hours. Drug use was detected more frequently in young males during daytime hours. Conclusions Driver risk profiles associated with alcohol use and drug use differ. Positive alcohol use is not a predictor of drug use when controlling for all other factors.

Amoeboid movement is one of the most widespread forms of cell motility that plays a key role in numerous biological contexts. While many aspects of this process are well investigated, the large cell-to-cell variability in the motile characteristics of an otherwise uniform population remains an open question that was largely ignored by previous models. In this article, we present a mathematical model of amoeboid motility that combines noisy bistable kinetics with a dynamic phase field for the cell shape. To capture cell-to-cell variability, we introduce a single parameter for tuning the balance between polarity formation and intracellular noise. We compare numerical simulations of our model to experiments with the social amoeba Dictyostelium discoideum. Despite the simple structure of our model, we found close agreement with the experimental results for the center-of-mass motion as well as for the evolution of the cell shape and the overall intracellular patterns. We thus conjecture that the building blocks of our model capture essential features of amoeboid motility and may serve as a starting point for more detailed descriptions of cell motion in chemical gradients and confined environments., Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe, 1014

We empirically study market integration and the propagation of shocks in the interconnected market of Nord Pool. We document an increasing trend towards market integration over recent decades in Nord Pool and identify clear cycles accounting for greater integration (larger transmission of shocks) in the cold seasons. Greater market integration permits a higher level of risk sharing between electricity markets and, as a result, can be expected to reduce the probability of energy crises and energy shortages occurring in any given market. Furthermore, we differentiate between shock propagation in the two tails of the price variation distribution and, so, distinguish downside risk from upside risk spillovers. Market spillovers following price increments are transmitted to a greater degree than are those following price reductions in the market. We also document asymmetries related both to the size of the transaction area and as to whether a given area behaves as a net-exporter or net-importer of electricity. For instance, we show that the larger the transaction area, the smaller are the volatility shocks on prices that it receives from the rest of the system.

Treballs Finals del Màster de Ciències Actuarials i Financeres, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2019-2020, Tutoria: Luis Ortiz Gracia, El presente trabajo tiene como objetivo describir e implementar modelos para la tarificación de seguros hipotecarios mediante técnicas de medición del riesgo de crédito basades en el “modelo de Merton”. Todo ello, ha sido realizado considerando el precio de la vivienda como estocástico, ya sea mediante un “Movimiento Browniano Geométrico” o mediante un “Modelo Factorial” que permite diferenciar el riesgo de fallida entre sistemático e idiosincrático. Por último, y como aportación innovadora, se propone aproximar el problema descrito mediante el “algoritmo de Tilley” utilizado habitualmente en la valoración de opciones financieras de estilo americano.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Josep Vives i Santa Eulàlia, [en] The aim of this project is to prove the two fundamental theorems of the theory of Lévy Processes: the Lévy-Khintchine Theorem and the Lévy-Itô Decomposition. We can interpret this two theorems as a description and classification of infinite divisible probability measures and Lévy processes, respectively. The importance of this type of probability measures and processes is that they appear in the modeling of random phenomena under certain reasonable hypothesis.

The Lee-Carter model is a useful dynamic stochastic model to represent the evolution of central mortality rates throughout time. This model only considers the uncertainty about the coefficient related to the mortality trend over time but not to the age-dependent coefficients. This paper proposes a fuzzy-random extension of the Lee-Carter model that allows quantifying the uncertainty of both kinds of parameters. As it is commonplace in actuarial literature, the variability of the time-dependent index is modeled as an ARIMA time series. Likewise, the uncertainty of the age-dependent coefficients is also quantified, but by using triangular fuzzy numbers. The consideration of this last hypothesis requires developing and solving a fuzzy regression model. Once the fuzzy-random extension has been introduced, it is also shown how to obtain some variables linked with central mortality rates such as death probabilities or life expectancies by using fuzzy numbers arithmetic. It is simultaneously shown the applicability of our developments with data of Spanish male population in the period 1970-2012. Finally, we make a comparative assessment of our method with alternative Lee-Carter model estimates on 16 Western Europe populations.

During cardiac diseases many types of anatomical and functional remodeling of cardiac tissue can occur. In this work, we focus on two conditions: hypoxia and fibrosis, which are part of complex pathological modifications that take place in many cardiac diseases (hypertrophic cardiomyopathy, hypertensive heart disease, and recurrent myocardial infarction) and respiratory diseases (obstructive pulmonary disease, obstructive sleep apnea, and cystic fibrosis). Using computational models of cardiac electrophysiology, we evaluate if the interplay between hypoxia and fibrosis is sufficient to trigger cardiac arrhythmia. We study the mechanisms behind the generation of ectopic beats, an arrhythmic trigger also known as premature ventricular contractions (PVCs), in regions with high hypoxia and fibrosis. First, we modify an electrophysiological model of myocytes of the human left ventricle to include the effects of hypoxia. Second, diffuse fibrosis is modeled by randomly replacing cardiac myocytes by non-excitable and non-conducting cells. The Monte Carlo method is used to evaluate the probability of a region to generate ectopic beats with respect to different levels of hypoxia and fibrosis. In addition, we evaluate the minimum size of three-dimensional slabs needed to sustain reentries for different stimulation protocols. The observed mechanism behind the initiation of ectopic beats is unidirectional block, giving rise to sustained micro-reentries inside the region with diffuse fibrosis and hypoxia. In summary, our results suggest that hypoxia and fibrosis are sufficient for the creation of a focal region in the heart that generates PVCs. We acknowledge support from CAPES by the grant 88881.065002/2014-01 of the Brazilian program Science without borders, and from MINECO of Spain under the Ramon y Cajal program with the grant number RYC-2012-11265

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: David Márquez Carreras, [en] At the beginning of the 70s, last century, physician scientists started to study, inside the studies about the state of matter, some mathematical structures called spin glasses. After that, and due to the need to go deeper in the knowledge of the study of the properties of these structures, mathematicians started to study them as well in order to understand their properties from a less physical point of view. In this paper we present an introduction to three of the easiest models of spin glasses. In chapter one we will introduce spin glasses, and we will see an example which will help us to understand better this concept. We will also introduce the basic concepts which we will use along this paper, such as free energy and the Gibbs’ measure. We will use the next chapters to study several easy models of spin glasses. In chapter two we will study model REM, which is possibly one of the existing easiest models. Chapters three and four contain details about Sherrington and Kirkpatrick models, with and without external field respectively. In chapter four we will also see how the action of a magnetic field is modelled in this kind of structures, and we will obtain different results in both models.

Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals and incorporate various individual characteristics of the policyholders by means of explanatory variables. Since the data set was collected over a longer time period (10 years), we also added each individual’s exposure to risk. To estimate the parameters of the three Sarmanov distributions, we analyze a pseudo-maximumlikelihood method. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM.

Greedy Randomized Adaptive Search Procedures (GRASP) are among the most popular metaheuristics for the solution of combinatorial optimization problems. While GRASP is a relatively simple and efficient framework to deal with deterministic problem settings, many real-life applications experience a high level of uncertainty concerning their input variables or even their optimization constraints. When properly combined with the right metaheuristic, simulation (in any of its variants) can be an effective way to cope with this uncertainty. In this paper, we present a simheuristic algorithm that integrates Monte Carlo simulation into a GRASP framework to solve the permutation flow shop problem (PFSP) with random processing times. The PFSP is a well-known problem in the supply chain management literature, but most of the existing work considers that processing times of tasks in machines are deterministic and known in advance, which in some real-life applications (e.g., project management) is an unrealistic assumption.

Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals and incorporate various individual characteristics of the policyholders by means of explanatory variables. Since the data set was collected over a longer time period (10 years), we also added each individual’s exposure to risk. To estimate the parameters of the three Sarmanov distributions, we analyze a pseudo-maximumlikelihood method. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM.

Consider the Erdos-Renyi random graph G(n, M) built with n vertices and M edges uniformly randomly chosen from the set of n2 edges. Let L be a set of positive integers. For any number of edges M 6n/2 + O(n 2/3 ), we compute – via analytic combinatorics – the number of isolated cycles of G(n, M) whose length is in L. Universite Paris Denis Diderot supported by ANR 2010 BLAN 0204 (Magnum). Partially supported by grants ANR 2010 BLAN 0204 (Magnum) and the Project PHC Procope ID- 57134837 “Analytic, probabilistic and geometric Methods for Random Constrained graphs”. Partially supported by the Project PHC Procope ID-57134837 “Analytic, probabilistic and geometric Methods for Random Constrained graphs”, by the FP7-PEOPLE-2013-CIG project CountGraph (ref. 630749), and the Spanish MICINN projects MTM2014-54745-P, MTM2014-56350-P

In this paper, we focus on a scenario in which a company or a set of companies conforming a supply network must deliver a complex product (service) composed of several components (tasks) to be processed on a set of parallel flow-shops with a common deadline. Each flow-shop represents the manufacturing of an independent component of the product, or the set of activities of the service. We assume that the processing times are random variables following a given probability distribution. In this scenario, the product (service) is required to be finished by the deadline with a user-specified probability, and the decision-maker must decide about the starting times of each component/task while minimizing one of the following alternative goals: (a) the maximum completion time; or (b) the accumulated deviations with respect to the deadline. A simheuristic-based methodology is proposed for solving this problem, and a series of computational experiments are performed.

Academics and policymakers have shown great interest in cross-national comparisons of intergenerational earnings mobility. However, producing consistent and comparable estimates of earnings mobility is not a trivial task. In most countries researchers are unable to observe earnings information for two generations. They are thus forced to rely upon imputed data from different surveys instead. This paper builds upon previous work by considering the consistency of the intergenerational correlation (ρ) as well as the elasticity (β), how this changes when using a range of different instrumental (imputer) variables, and highlighting an important but infrequently discussed measurement issue. Our key finding is that, while TSTSLS estimates of β and ρ are both likely to be inconsistent, the magnitude of this problem is much greater for the former than it is for the latter. We conclude by offering advice on estimating earnings mobility using this methodology., Survey Research Methods, Vol 10, No 2 (2016)

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Josep Vives i Santa Eulàlia, In our project, we have analyzed the working of the Spanish electricity market, the operators which participate on it, the regulated components, market prices and the existing risk. Likewise, it will be developed a model to quantify and reduce the electricity company risk due to establish a fixed price for the client. The ideal target is a high tension client with a six period rate hired since January 1 st to December 31 st 2017. The model is designed through random variables and probabilities based on historical series. This model will develop an annual cost in raw material, which could be extrapolated to a cost per hour. This process will be repeat until achieving results. This program is going to be developed with Excel device and programmed by “Basic Visual” language. This tool will provide enough information to the company to take a decision about offering a fixed priced to the client. In this case which price could be offer assuming the risks.

Understanding human mobility is of vital importance for urban planning, epidemiology, and many other fields that draw policies from the activities of humans in space. Despite the recent availability of large-scale data sets of GPS traces or mobile phone records capturing human mobility, typically only a subsample of the population of interest is represented, giving a possibly incomplete picture of the entire system under study. Methods to reliably extract mobility information from such reduced data and to assess their sampling biases are lacking. To that end, we analyzed a data set of millions of taxi movements in New York City. We first show that, once they are appropriately transformed, mobility patterns are highly stable over long time scales. Based on this observation, we develop a supersampling methodology to reliably extrapolate mobility records from a reduced sample based on an entropy maximization procedure, and we propose a number of network-based metrics to assess the accuracy of the predicted vehicle flows. Our approach provides a well founded way to exploit temporal patterns to save effort in recording mobility data, and opens the possibility to scale up data from limited records when information on the full system is required., EU-LASAGNE Project (Contract 318132 (STREP)), Spain. Ministerio de Economia y Competitividad (Grant FIS2012-38266-C02-02), Generalitat de Catalunya (FI Program 2014-SGR-00608), Enel Foundation, Audi Volkswagen, SENSEable City Lab Consortium

Departament de Matemàtiques. Codis assignatura: RA10, RL0906

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2014, Director: Josep Vives i Santa Eulàlia, The aim of this final project is to study the pricing of zero-coupon bonds of different interest rate models in a continuous-time market in the absence of arbitrage opportunities, specifically, the Vasicek model and the Cox-Ingersoll-Ross model. First, this study needs to analyze the basis of the stochastic modeling of continuous-time market which includes to study some notions about the stochastic calculus. So, first the chapters 1 and 2 have some useful concepts and results of stochastic calculus like the Brownian motions, the stochastic integrals, the Itô calculus, the stochastic differential equations... Then, in the chapter 3 some economic concepts, the model of continuous-time market and the concept of portfolio self-financing, are defined; and also, this Black-Scholes pricing are studied. Later, in the chapter 4, some common models short term interest rate models are introduced. Last, in the chapter 5, the pricing of zero-coupon bonds are studied following the two named models in the former chapter, the Vasicek model and Cox-Ingersoll-Ross model, using pricing from chapter 3. During all the project, we suppose all the affirmations about finite random variables and stochastic processes are true P almost surely. To sum up, we have used different resources but overall, we have based on the books Introduction to stochastic calculus applied to finance ([Lam]) and An elementary introduction to stochastic interest rate modeling ([Pri]).

This paper develops life insurance pricing with different representation of its two sources of uncertainty: stochastic behaviour of mortality of the insured and fuzzy quantification of interest rates within the time horizon. Concretely we analyse endowment contracts, which are present in several financial real - world contexts as residential mortgage loans or retirement plans. We show that modelling the present value of these contracts with fuzzy random variables allows a well - founded quantification of their fair price and the risk resulting from the uncertainty of mortality and discounting rates. To do this, we firstly describe fuzzy random variables and some associated measures (mathematical expectation, variance, distribution function and quantiles) are defined. Subsequently the present value of a endowment contract (pure and mixed) is modelled with fuzzy random variables. Finally we show how the price and risk measures for endowment portfolios can be obtained

The phenomenon of human migration is certainly not new and it has been studied from a variety of perspectives. Yet, the attention on human migration and its determinant has not been fading over time as confirmed by recent contributions (see for instance Cushing and Poot 2004 and Rebhun and Raveh 2006). In this paper we combine the recent theoretical contributions by Douglas (1997) and Wall (2001) with the methodological advancements of Guimarães et al. (2000, 2003) to model inter-municipal migration flows in the Barcelona area. In order to do that, we employ two different types of count models, i.e. the Poisson and negative binomial and compare the estimations obtained. Our results show that, even after controlling for the traditional migration factors, QoL (measured with a Composite Index which includes numerous aspects and also using a list of individual variables) is an important determinant of short distance migration movements in the Barcelona area.

En aquesta tesi s'estudien diferents problemes en el camp de la combinatòria i la teoria de grafs, utilitzant el mètode probabilístic. Aquesta tècnica, introduïda per Erdős , ha esdevingut una eina molt potent per tal de donar proves existencials per certs problemes en diferents camps de les matemàtiques on altres mètodes no ho han aconseguit. Un dels seus principals objectius és l'estudi del comportament de les variables aleatòries. El cas en que aquestes variables compten el nombre d'esdeveniments dolents que tenen lloc en una estructura combinatòria és de particular interès. La idea del Paradigma de Poisson és estimar la probabilitat que tots aquests esdeveniments dolents no succeeixin a la vegada, quan les dependències entre ells són febles o escasses. En tal cas, aquesta probabilitat s'hauria de comportar de forma similar al cas on tots els esdeveniments són independents. El Lema Local de Lovász o la Desigualtat de Suen són exemples d'aquesta idea. L'objectiu de la tesi és estudiar aquestes tècniques ja sigui proveint-ne noves versions, refinant-ne les existents per casos particulars o donant-ne noves aplicacions. A continuació s'enumeren les principals contribucions de la tesi. La primera part d'aquesta tesi estén un resultat d' Erdős i Spencer sobre transversals llatins. Els autors proven que qualsevol matriu d'enters on cap nombre apareix massa vegades, admet un transversal on tots els nombres són diferents. Això equival a estudiar els aparellaments multicolors en aresta-coloracions de grafs complets bipartits. Sota les mateixes hipòtesis que, es donen resultats sobre el nombre d'aquests aparellaments. Les tècniques que s'utilitzen estan basades en l'estratègia desenvolupada per Lu i Székely. En la segona part d'aquesta tesi s'estudien els codis identificadors. Un codi identificador és un conjunt de vèrtexs tal que tots els vèrtexs del graf tenen un veïnatge diferent en el codi. Aquí s'estableixen cotes en la mida d'un codi identificador mínim en funció dels graus i es resol parcialment una conjectura de Foucaud et al.. En un altre capítol, es mostra que qualsevol graf suficientment dens conté un subgraf que admet un codi identificador òptim. En alguns casos, provar l'existència d'un cert objecte és trivial. Tot i així, es poden utilitzar les mateixes tècniques per obtenir resultats d'enumeració. L'estudi de patrons en permutacions n'és un bon exemple. A la tercera part de la tesi es desenvolupa una nova tècnica per tal d'estimar el nombre de permutacions d'una certa llargada que eviten còpies consecutives d'un patró donat. En particular, es donen cotes inferiors i superiors per a aquest nombre. Una de les conseqüències és la prova de la conjectura CMP enunciada per Elizalde i Noy així com nous resultats en el comportament de la majoria dels patrons. En l'última part de la tesi s'estudia la Conjectura Lonely Runner, enunciada independentment per Wills i Cusick i que té múltiples aplicacions en diferents camps de les matemàtiques. Aquesta coneguda conjectura diu que per qualsevol conjunt de corredors que corren al llarg d'un cercle unitari, hi ha un moment on tots els corredors estan suficientment lluny de l'origen. Aquí, es millora un resultat de Chen ampliant la distància de tots els corredors a l'origen. També s'estén el teorema del corredor invisible de Czerwiński i Grytczuk ., In this thesis we study different problems in combinatorics and in graph theory by means of the probabilistic method. This method, introduced by Erdös, has become an extremely powerful tool to provide existential proofs for certain problems in different mathematical branches where other methods had failed utterly. One of its main concerns is to study the behavior of random variables. In particular, one common situation arises when these random variables count the number of bad events that occur in a combinatorial structure. The idea of the Poisson Paradigm is to estimate the probability of these bad events not happening at the same time when the dependencies among them are weak or rare. If this is the case, this probability should behave similarly as in the case where all the events are mutually independent. This idea gets reflected in several well-known tools, such as the Lovász Local Lemma or Suen inequality. The goal of this thesis is to study these techniques by setting new versions or refining the existing ones for particular cases, as well as providing new applications of them for different problems in combinatorics and graph theory. Next, we enumerate the main contributions of this thesis. The first part of this thesis extends a result of Erdös and Spencer on latin transversals [1]. They showed that an integer matrix such that no number appears many times, admits a latin transversal. This is equivalent to study rainbow matchings of edge-colored complete bipartite graphs. Under the same hypothesis of, we provide enumerating results on such rainbow matchings. The second part of the thesis deals with identifying codes, a set of vertices such that all vertices in the graph have distinct neighborhood within the code. We provide bounds on the size of a minimal identifying code in terms of the degree parameters and partially answer a question of Foucaud et al. On a different chapter of the thesis, we show that any dense enough graph has a very large spanning subgraph that admits a small identifying code. In some cases, proving the existence of a certain object is trivial. However, the same techniques allow us to obtain enumerative results. The study of permutation patterns is a good example of that. In the third part of the thesis we devise a new approach in order to estimate how many permutations of given length avoid a consecutive copy of a given pattern. In particular, we provide upper and lower bounds for them. One of the consequences derived from our approach is a proof of the CMP conjecture, stated by Elizalde and Noy as well as some new results on the behavior of most of the patterns. In the last part of this thesis, we focus on the Lonely Runner Conjecture, posed independently by Wills and Cusick and that has multiple applications in different mathematical fields. This well-known conjecture states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a moment where all of them are far enough from the origin. We improve the result of Chen on the gap of loneliness by studying the time when two runners are close to the origin. We also show an invisible runner type result, extending a result of Czerwinski and Grytczuk.

El requerimiento de capital de solvencia del riesgo de primas y reservas no vida bajo el enfoque del modelo estándar viene determinada por la fórmula especificada en el último estudio de impacto cuantitativo. Dicha fórmula toma en consideración una segmentación del riesgo de suscripción correspondiente a una clasificación por líneas de negocio, para las que son considerados unos parámetros. La fórmula puede ser utilizada con los parámetros propuestos por el regulador como proxy de mercado, o ser reparametrizada atendiendo a la experiencia propia de la entidad. Sin embargo, a pesar de que el propio estudio de impacto cuantitativo indica cómo deben ser estimados dichos parámetros propios, la variable aleatoria implícita en la fórmula estándar para el riesgo de primas y reservas no queda claramente definida. En este trabajo mostramos cuál es la variable aleatoria implícita en dicha fórmula, y presentamos una nueva propuesta de variable aleatoria con la finalidad de remarcar cuál es la influencia que tiene sobre el requerimiento de capital, y sobre los parámetros derivados de la fórmula estándar para el riesgo tratado, la elección de la variable de referencia. Los resultados obtenidos muestran la importancia de la elección de una variable aleatoria que sea representativa del riesgo a tratar como paso previo a la definición de un modelo interno.

In this paper a dissimilarity index between statistical populations is proposed without the hypothesis of a specific statistical model. We assume that the studied populations differ on some relevant features which are measured through convenient parameters of interest. We assume also that we dispose of adequate estimators for these parameters. To measure the differences between populations with respect to the parameters of interest, we construct an index inspired on some properties of the information metric which are also presented. Additionally, we consider several examples and compare the obtained dissimilarity index with some other distances, like Mahalanobis or Siegel distances.

This study deals with the statistical properties of a randomization test applied to an ABAB design in cases where the desirable random assignment of the points of change in phase is not possible. In order to obtain information about each possible data division we carried out a conditional Monte Carlo simulation with 100,000 samples for each systematically chosen triplet. Robustness and power are studied under several experimental conditions: different autocorrelation levels and different effect sizes, as well as different phase lengths determined by the points of change. Type I error rates were distorted by the presence of autocorrelation for the majority of data divisions. Satisfactory Type II error rates were obtained only for large treatment effects. The relationship between the lengths of the four phases appeared to be an important factor for the robustness and the power of the randomization test.

[eng] Dependence between random variables is studied at various levels in the first part, while the last two chapters are devoted to the construction of bivariate distributions via principal components. Chapter 1 of Preliminaries is devoted to general dependence concepts (Fréchet classes, copulas, and parametric families of distributions). In Chapter 2, we generalize the union and intersection operations of two distance matrices to symmetric nonnegative definite matrices. These operations are shown to be useful in the geometric interpretation of Related Metric Scaling (RMS ), and possibly in other approaches of Multivariate Analysis. They show relevant properties that are studied in this chapter. The behaviour of the operations is, in some way, analogous to that presented by the intersection and union between vector spaces; in particular, we prove that the intersection of orthogonal matrices is the null matrix, while the union is the direct sum of the matrices. Matrices that share their eigenvectors form an equivalence class, and a partial order relation is defined. This class is closed for the union and intersection operations. A continuous extension of these operations is presented in Chapter 3. Infinite matrices are studied in the context of bounded integral operators and numerical kernels. We put the basis for extending RMS to continuous random variables and, hence, infinite matrices. The starting point is Mercer's Theorem, which ensures the existence of an orthogonal expansion of the covariance kernel K (s, t) = min {F (s) , F (t)} - F (s) F (t), where F is the cumulative distribution function of each marginal variable. The sets of eigenvalues and eigenfunctions of K, whose existence is ensured by the cited theorem, allow us to define a product between symmetric and positive (semi)definite kernels, and, further, to define the intersection and the union between them. Results obtained in the discrete instance are extended in this chapter to continuous variables, with examples. Such covariance kernels (symmetric and positive definite) are associated with symmetric and positive quadrant dependent (PQD) bivariate distributions. Covariance between functions of bounded variation defined on the range of some random variables, joined by distributions of this type, can be computed by means of their cumulative distribution functions. In Chapter 4, further consequences are obtained, especially some relevant relations between the covariance and the Fréchet bounds, with a number of results that can be useful in the characterization of independence as well as in testing goodness-of-fit. The intersection of two kernels (defined in Chapter 3) is a particular instance of the covariance between functions. Covariance is a quasiinner product defined through the joint distribution of the variables involved. A measure of affinity between functions with respect to H is defined, and also studied. In Chapter 5, from the concept of affinity between functions via an extension of the covariance, we define the dimension of a distribution, we relate it to the diagonal expansion and find the dimension for some parametric families. Diagonal expansions of bivariate distributions (Lancaster) allows us to construct bivariate distributions. It has proved to be adequate for constructing Markov processes, and has also been applied to engineering problems among other uses. This method has been generalized using the principal dimensions of each marginal variable that are, by construction, canonical variables. We introduce in Chapter 6 the theoretical foundations of this method. In Chapter 7 we study the bivariate, symmetric families obtained when the marginals are Uniform on (0, 1), Exponential with mean 1, standard Logistic, and Pareto (3,1). Conditions for the bivariate density, first canonical correlation and maximum correlation of each family of densities are given in some cases. The corresponding copulas are obtained., [cat] Al Capítol 1 de Preliminars es revisen conceptes de dependència generals (classes de Fréchet, còpules, i famílies paramètriques de distribucions). Al Capítol 2, generalitzem les operacions unió i intersecció de dues matrius de distàncies a matrius simètriques semidefinides positives qualssevol. Aquestes operacions s'han mostrat d'utilitat en la interpretació geomètrica del Related Metric Scaling (RMS), i possiblement en altres tècniques d'Anàlisi Multivariant. S'estudien llur propietats que són similars, en alguns aspectes, a les de la unió i intersecció de subespais vectorials. Al Capítol 3 es presenta una extensió al continuu d'aquestes operacions, mitjançant matrius infinites en el context dels operadors integrals acotats i nuclis numèrics. S'estableix la base per a extendre el RMS a variables contínues i, per tant, a matrius infinites. Es parteix del Teorema de Mercer el qual assegura l'existència d'una expansió ortogonal del nucli de la covariança K (s, t) = min {F (s), F (t)} - F (s) F (t), on F és la funció de distribució de cada variable marginal. Els conjunts de valors i funcions pròpies d'aquest nucli ens permeten definir un producte entre nuclis i la intersecció i unió entre nuclis simètrics semidefinits positius. Tals nuclis de covariança s'associen amb distribucions bivariants també simètriques i amb dependència quadrant positiva (PQD). El producte de dos nuclis és un cas particular de covariança entre funcions, que es pot obtenir a partir de les distribucions conjunta i marginals, com s'estudia al Capítol 4 per a funcions de variació afitada, fixada la distribució bivariant H. S'obtenen interessants relacions amb les cotes de Fréchet. Aquesta covariança entre funcions és un producte quasiescalar a l'espai de funcions de variació afitada i permet definir una mesura d'afinitat. Al Capítol 5 aquesta H-afinitat s'utilitza per definir la dimensió d'una distribució. Les components principals d'una variable (Capítol 6) s'utilitzen com a variables canòniques a l'expansió diagonal de Lancaster (Capítol 7 i últim) per a construïr distribucions bivariants amb marginals Uniformes al (0,1), Exponencial de mitjana 1, Logística estàndard, i Pareto (3,1). S'obtenen condicions per la densitat bivariant, correlacions canòniques i correlació màxima per cada família. S'obtenen les còpules corresponents.

Se comenta el significado de la selección o asignación aleatoria, randomización, en la investigación clínica. Se enumeran las bases teóricas, las implicaciones prácticas de la aleatoriedad, y su influencia en el diseño de la investigación. A continuación se comenta el diseño del muestreo propiamente dicho y se describe la realización práctica del muestreo aleatorio simple y equilibrado por bloques. Se discuten las ventajas de muestreo estratificado y en racimos para terminar con unas anotaciones sobre los muestreos no aleatorios y el tratamiento de la información perdida. Se destaca la importancia de la randomización para la realización de una investigación clínica correcta.

Esta Memoria es una aportación al Análisis Multivariante y su aplicación a la Biología. Los numerosos índices de disimilaridad y distancias que se utilizan en Estadística y son aplicados en Genética, Antropología, Ecología, etc., me han motivado a intentar estudiar una distancia entre poblaciones estadísticas paramétricas, de aplicación general, y que posea buenas propiedades matemáticas.En la primera parte (cap. 1 al 6), se desarrolla esta distancia estadística, definible para una clase muy general de funciones de densidad paramétricas, a través de la matriz de información de Fisher, hallando algunas de sus propiedades básicas y calculándola para ciertas distribuciones de probabilidad concretas. En la segunda parte (cap. 7 al 9), se aplican algunos de los resultados obtenidos, proponiendo una metodología estadística para el tratamiento de tablas de contingencia multidimensionales, asociadas a experiencias etológicas, ilustrándolo con el estudio, de la conducta agonística del lugano. También se propone un algoritmo utilizable para el diagnóstico de enfermedades, a partir de los resulta¬dos de unos análisis, aplicándolo al diagnóstico de ciertas enfermedades hematológicas a través de la interpretación de mielogramas.Finalmente se considera una alternativa al test "t" de Student para muestras independientes y se ilustra con el estudio de la relación entre la alcohol deshidrogenasa y el tamaño en "Drosophila melanogaster".

Sobre els dos primers moments de la mesura d'un joc d'atzar https://doi.org/10.1214/aoms/1177730490

Academics and policymakers have shown great interest in cross-national comparisons of intergenerational earnings mobility. However, producing consistent and comparable estimates of earnings mobility is not a trivial task. In most countries researchers are unable to observe earnings information for two generations. They are thus forced to rely upon imputed data instead. This paper builds upon previous work by considering the consistency of the intergenerational correlation (ρ) as well as the elasticity (β), how this changes when using a range of different instrumental (imputer) variables, and highlighting an important but infrequently discussed measurement issue. Our key finding is that, while TSTSLS estimates of β and ρ are both likely to be inconsistent, the magnitude of this problem is much greater for the former than it is for the latter. We conclude by offering advice on estimating earnings mobility using this methodology.

The Sarmanov family of distributions can provide a good model for bivariate random variables and it is used to model dependency in a multivariate setting with given marginals. In this paper, we focus our attention on the bivariate Sarmanov distribution and copula with different truncated extreme value marginal distributions. We compare a global estimation method based on maximizing the full log-likelihood function with the estimation based on maximizing the pseudolog- likelihood function for copula (or partial estimation). Our aim is to estimate two statistics that can be used to evaluate the risk of the sum exceeding a given value. Numerical results using a real data set from the motor insurance sector are presented.

Treball de Fi de Grau en Ciències Empresarials - Management. Curs 2018-2019 Tutors: Juan José Ganuza, Joaquín Catalán Núñez Este trabajo muestra, a través de una investigación empírica, las particularidades del ciclismo y las diferencias que se producen entre los ganadores de etapa de las principales competiciones internacionales. Tras aplicar un modelo econométrico, los resultados muestran que cuando la prueba presenta un elevado desnivel positivo acumulado, el vencedor es significativamente más longevo que el ciclista que cruza la línea de meta en primera posición en etapas llanas. Sin embargo, las variables relacionadas con el día de competición no son capaces de formar un patrón que pueda predecir con suficiente precisión qué edad tendrá el ganador.

In a (1 : q) Maker-Breaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Łuczak [Bednarska, M., and T. Łuczak, Biased positional games for which random strategies are nearly optimal, Combinatorica, 20 (2000), 477–488], who studied biased H-games, we prove general winning criteria for Maker and Breaker and a hypergraph generalization of their result. Furthermore, we study the biased version of a strong generalization of the van der Waerden games introduced by Beck [Beck, J., Van der Waerden and Ramsey type games, Combinatorica, 1 (1981), 103–116] and apply our criteria to determine the threshold bias of these games up to constant factor. As in the result of [Bednarska, M., and T. Łuczak, Biased positional games for which random strategies are nearly optimal, Combinatorica, 20 (2000), 477–488], the random strategy for Maker is again the best known strategy.