Operations on Risk Variables

In the article the author considers and analyzes operations and functions on risk variables. She takes into account the following variables: the sum of risk variables, its product, multiplication by a constant, division, maximum, minimum and median of a sum of random variables. She receives the formulas for probability distribution and basic distribution parameters. She conducts the analysis for dependent and independent random variables. She propose the examples of the situations in the economy and production management of risk modelled by this operations. The analysis is conducted with the way of mathematical proving. Some of the formulas presented are taken from the literature but others are the permanent results of the author.

Análisis y preparación estadística de variables para el diseño de un modelo credit score de gestión de riesgo de crédito

El presente estudio busca enfatizar la labor previa a la construcción de cualquier modelo de gestión de riesgo crediticio basado en un sistema tipo scoring. Esta importante fase inicial involucra la identificación de las fuentes de información, la verificación de la cantidad y calidad de los datos, la determinación y tipificación de variables cualitativas, cuantitativas, demográficas, así como la verificación y cuantificación del poder discriminante de dichas variables respecto el objetivo planteado. Con este fin se profundiza en el análisis estadístico a nivel descriptivo, en forma individual y conjunta de los datos, además de bosquejar los pasos esenciales en la arquitectura de un modelo credit score de gestión de riesgo crediticio.

Gestión de riesgo de crédito de la Cooperativa de Ahorro y Crédito Maquita Cushunchic: análisis y preparación estadística de variables para el diseño de un modelo Credit Score de cartera de consumo

El presente estudio busca analizar y preparar estadísticamente un conjunto de variables para el diseño de un modelo de aprobación CREDIT SCORE de cartera de consumo, tipo probabilístico, que apoye al oficial de crédito en la toma de la decisión antes de conceder o no un crédito de consumo; para que la decisión no sea subjetiva sino objetiva, medible (probabilística) apoyada en una ecuación que contenga sustento teórico y empírico dado por la base de datos histórica de la Cooperativa de ahorro y crédito Maquita Cushunchic. En la presente tesis partimos con fundamentación teórica que sustenta nuestro trabajo de investigación. En el segundo capítulo se realiza un diagnostico situacional de la empresa, donde se define la visión, la misión y definición de temas estratégicos. En el tercer capítulo realizaremos un análisis y preparación estadística de variables para el diseño de un modelo de aprobación CREDIT SCORE de cartera de consumo, esta fase involucra “la identificación de las fuentes de información, la verificación de cantidad y calidad de los datos, la determinación y tipificación de variables cualitativas, cuantitativas y demográficas, así como la verificación y cuantificación del poder discriminante de dichas variables respecto al objetivo planteado” 1, todo esto se lo realiza con el objetivo de aplicar un concepto de sistemas de calificación de crédito que se define de la siguiente manera: “la calificación supone que el desempeño de los prestamos futuros con características dadas, será parecido al desempeño de los prestamos pasados con características similares"2. Lo que se busca finalmente es que el modelo sea una herramienta de apoyo empírico que ayude a la toma de decisiones antes de conceder o no un credito. Finalmente termina este trabajo formulando conclusiones y recomendaciones.

Desarrollo de un Score de crédito para el financiamiento automotríz, con base en el análisis estadístico de variables

El mercado automotriz en el Ecuador es uno de los sectores que dinamiza la economía; a través de la producción e importación de vehículos y la comercialización de estos. El crecimiento de este sector en los últimos años ha sido constante y sostenido, al igual que el incremento de financiamientos otorgados a los consumidores o sujetos de crédito para la compra de un vehículo. El presente trabajo tiene como propósito el desarrollo de un score de crédito para el financiamiento automotriz que permita identificar a los buenos y malos solicitantes y así decidir entre otorgar o no el crédito. Para ello se han desarrollado cuatro capítulos. En el primer capítulo se realiza una introducción sobre el mercado automotriz su producción, niveles de importación, cadena de distribución, y otros; además de la composición del parque automotor y problemas de movilidad y el comportamiento de compra y los niveles de crédito automotriz. En el segundo capítulo se trata sobre la base de datos de las organizaciones y los tipos de variables que pueden contener y se explica los tipos de modelos de regresiones que se pueden realizar. En el tercer capítulo se define al modelo de score de crédito y los pasos a seguir para la construcción de este. En el cuarto capítulo se desarrollan todos los pasos para la construcción del score de crédito y en quinto capítulo se encuentran las conclusiones y recomendaciones del presente trabajo.

Variables associated with nest survival of Golden-winged Warblers (Vermivora chrysoptera) among vegetation communities commonly used for nesting

Among shrubland- and young forest-nesting bird species in North America, Golden-winged Warblers (Vermivora chrysoptera) are one of the most rapidly declining partly because of limited nesting habitat. Creation and management of high quality vegetation communities used for nesting are needed to reduce declines. Thus, we examined whether common characteristics could be managed across much of the Golden-winged Warbler’s breeding range to increase daily survival rate (DSR) of nests. We monitored 388 nests on 62 sites throughout Minnesota, Wisconsin, New York, North Carolina, Pennsylvania, Tennessee, and West Virginia. We evaluated competing DSR models in spatial-temporal (dominant vegetation type, population segment, state, and year), intraseasonal (nest stage and time-within-season), and vegetation model suites. The best-supported DSR models among the three model suites suggested potential associations between daily survival rate of nests and state, time-within-season, percent grass and Rubus cover within 1 m of the nest, and distance to later successional forest edge. Overall, grass cover (negative association with DSR above 50%) and Rubus cover (DSR lowest at about 30%) within 1 m of the nest and distance to later successional forest edge (negative association with DSR) may represent common management targets across our states for increasing Golden-winged Warbler DSR, particularly in the Appalachian Mountains population segment. Context-specific adjustments to management strategies, such as in wetlands or areas of overlap with Blue-winged Warblers (Vermivora cyanoptera), may be necessary to increase DSR for Golden-winged Warblers.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

Bryophyte diversity and community structure on thatched roofs of the Holnicote Estate, Somerset, U.K.

We investigated patterns of bryophyte species richness and community structure, and their relation to roof variables, on thatched roofs of the Holnicote Estate, South Somerset. Thirty-two bryophyte species were recorded from 28 sampled roofs, including the globally rare and endangered thatch moss, Leptodontium gemmascens. Multiple regression analyses revealed that thatch age has a highly significant positive effect on the number of species present, accounting for nearly half the observed variation in species richness after removal of outliers. Aspect has a slight and marginally significant effect on species diversity (accounting for an additional 6% of variation), with north-facing samples having slightly more species. Age also has a significant impact on total bryophyte cover after removal of outlying observations. TWINSPAN analysis of bryophyte cover data suggests the existence of at least five discrete communities. Simple Discriminant Analyses indicate that these communities occupy different ecological subspaces as defined by the measured roof variables, with pitch, aspect and thatch age emerging as especially significant attributes. Contingency Analysis indicates that some communities are disfavoured by water reed as compared to wheat straw. The findings are significant for understanding the structure of bryophyte communities, for evaluating the effect of bryophyte cover on thatch performance, and for conservation of thatch communities, especially those harbouring rare species.

Synthesis, crystal structure and hydrolysis of a dinuclear copper(II) complex constructed by N2O donor Schiff base and 4,4 '-bipyridine: discrete supra-molecular ensembles vs. oligomers

The tridentate Schiff base ligand, 7-amino-4-methyl-5-aza-3-hepten-2-one (HAMAH), prepared by the mono-condensation of 1,2diaminoethane and acetylacetone, reacts with Cu(BF4)(2) center dot 6H(2)O to produce initially a dinuclear Cu(II) complex, [{Cu(AMAH)}(2) (mu-4,4'-bipyJ](BF4)(2) (1) which undergoes hydrolysis in the reaction mixture and finally produces a linear polymeric chain compound, [Cu(acac)(2)(mu-4,4'-bipy)](n) (2). The geometry around the copper atom in compound 1 is distorted square planar while that in compound 2 is essentially an elongated octahedron. On the other hand, the ligand HAMAH reacts with Cu(ClO4)(2) center dot 6H(2)O to yield a polymeric zigzag chain, [{Cu(acac)(CH3OH)(mu-4,4'-bipy)}(ClO4)](n) (3). The geometry of the copper atom in 3 is square pyramidal with the two bipyridine molecules in the cis equatorial positions. All three complexes have been characterized by elemental analysis, IR and UV-Vis spectroscopy and single crystal X-ray diffraction studies. A probable explanation for the different size and shape of the reported polynuclear complexes formed by copper(II) and 4,4'-bipyridine has been put forward by taking into account the denticity and crystal field strength of the blocking ligand as well as the Jahn-Teller effect in copper(II). (c) 2007 Elsevier Ltd. All rights reserved.