PROBABILITY

Author: EL HALIMI RACHID.
Year: 2004.
University: BARCELONA.
Place of defense: FACULTAD DE BIOLOGIA.
Place of preparation: UNIVERSITAT DE BARCELONA.

Summary: In this research presents a "workshop" for advanced data analysis in the context of the models mixed with arrays structured varianzas-covarianzas of the random effects and / or waste. The adjustment of these models has revealed some concerns about the sensitivity of the inferences regarding the assumptions of the model, especially when they do not satisfy the usual assumptions about normalcy waste and random factors. The main purpose of the work has been the study of the validity of the use of non-linear mixed models to analyze data from repeated measures and discuss the robustness of inferential parametric approach based on the approximation proposed by lindstrom and Bates (1990), and to propose and evaluate possible alternatives to it, based on the bootstrap methodology. It also discusses the best way to generate the bootstrap samples from longitudinal data under mixed models, and is an adaptation of the methodology to bootstrap adjustment methods in two phases, as STS (Standard two-stage) and GTS (Global two - stage). The simulation results confirm that the parametric approach based on the assumption of normality is not reliable when the distribution of the variable studied seriously deviates from the norm. Specifically, the approximate confidence intervals based on a linear approximation, and generally the results aintóticos of utmost versoimilitud, there are robust compared to the deviation from the assumptions of normality of the data, even show them to relatively large sizes. The method "bootstrap" provides an estimate of the parameters in terms of the range and breadth of its coverage relatively more appropriate for the classic method, based on the assumption of normal variable studied.

Author: MONLEON GETINO ANTONIO.
Year: 2005.
University: BARCELONA.
Place of defense: FACULTAD DE BIOLOGÍA.
Place of preparation: FACULTAD DE BIOLOGIA (UB).

Author: VIVO MOLINA JUANA MARÍA.
Year: 2005.
University: GRANADA.
Place of defense: FACULTAD DE CIENCIAS ECONÓMICAS Y EMPRESARIALES.
Place of preparation: FACULTAD DE CIENCIAS ECONÓMICAS Y EMPRESARIALES.

Summary: This report consists of five chapters with its findings. In the first four introduces the tools and addresses the properties logconcavidad of probability models, and the last chapter is for the economic approach and its application in valuation. In particular, the first chapter introduces some probability models univariate and bivariate usual theory of valuation, as well as some exponential bivariate models used in the modeling process risk dependents. It also includes definitions and basic properties of logconcavidad that are used along the memory implemented at the end of this chapter to the univariate models usual theory of valuation. To begin the study of the properties of extreme bivariate probabilistic models, in the second chapter examines the most common models exponential bivariate through the widespread mixtures of two or three exponential, expanding existing results in the literature through the classification of these mixtures, and applied to the ends of the statistical models exponential bivariate. In addition, some of these extreme models exponential bivariate still a mixture of four generalized exponential. Therefore, in the third chapter discusses these mixtures extending the previous chapter, obtained the characterization of the four mixtures generalized exponential to be a probability model, as well as the classification of the logconcavidad of them, apply to extremes of some models exponential bivariate. Moreover, not all statistical extremes of the bivariate models are mixtures of generalized exponential. For example, in the exponential model of bivariate Friday and Patil appear mixtures gamma and exponential, which are discussed in the fourth chapter. It also discusses another extension of the mixtures through widespread exponential models Weibul bivariate; these mixtures of Weibul have been used in economics to model the price index of market Hang-Seng. Also included in this chapter properties logconcavidad of statistical extremes, for data models in the first chapter, which do not conform to any kind of mixture. To end this memory, with the idea of applying the statistical extremes and properties logconcavidad in economics, and in particular valuation theory, in chapter five examines alternative valuation methods, through the functions of survival and the statistical outliers. Here, we propose a new method, called the method of valuation of the two survival functions, and compared with the known method of valuation of the two distribution functions. Also, we studied the behavior of this new method using the weighted models used to adjust or correct the market value, and further extending the range of such models weighted in two directions: through the functions of survival and using a new technique for generating weights. However, the use of models weighted does not resolve completely the problem of finding market value, it is proposed the use of statistical extremes are analyzed by these valuations proportional statistical through both valuation methods and utility properties logconcavidad. We conclude this chapter with an application of the téncicas proposed therein.