Implementación del càlculo de polinomios zonales y aplicaciones en análisis multivariante

En este trabajo se describe la implementación de un algoritmo para el cálculo de polinomios zonales, así como dos aplicaciones explícitas de éstos en el ámbito del análisis multivariante. Concretamente, esta implementación permite obtener resultados de sumación aproximados para funciones hipergeométricas de argumento matricial que, a su vez, pueden utilizarse en la génesis de distribuciones multivariantes discretas con frecuencias simétricas. De igual forma, se pone en práctica un conocido resultado teórico que caracteriza la distribución de la menor raíz característica de una matriz aleatoria con distribución de Wishart

A Field Procedure for the Assessment of the Centring Uncertainty of Geodetic and Surveying Instruments

The uncertainty evaluation of survey measurements is a daily and essential task in any surveying work. The result of a measurement is, in fact, only complete when accompanied by a statement of its uncertainty. Miscentring, or centring error, is one of the sources of uncertainty in every basic survey measurement which may have a great effect on horizontal angle measurement for short distances. In the literature, different terms and values are considered to refer to this source of uncertainty. Standard ISO 17123 provides different procedures for assessing the measurement uncertainty of geodetic and surveying instruments, with the aim of checking their suitability for the intending and immediate task in field conditions. ISO 17123 is aware of the importance of uncertainty in the instrument centring, but it does not propose any standardised procedure for its assessment. In this study, we propose such a procedure following a Type A evaluation (through the statistical analysis of series of observations), avoiding using values from Type B evaluations (from manufacturer’s specifications, handbooks, personal experiences, etc.) that could be unsuitable for the conditions of the task. Uncertainty can be individualised for a particular instrument (which includes the plummet type), ground mark, operator, and other factors on which the results could be dependent. The testing methodology includes a configuration of the test field, measurements, and calculation, following the structure of each part of the standard ISO 17123. An experimental application is included with two different total stations, which also includes a statistical analysis of the results.The work of J.R.-R. was funded by the Vice Chancellor of Relations with Society and Labour Insertion of the University of Jaén (Grant No. 06190505N5 IFT1). The article processing charge (APC) was funded by the Research Groups “Ingeniería Cartográfica” and “Microgeodesia Jaén” (Grant Nos. PAIDI-TEP-164 and PAIDI-RNM-282 from the Regional Government of Andalucía) which also received financial support from PAIUJA R5/1/2017 of the University of Jaén

Heterogeneous contributions of change in population distribution of body mass index to change in obesity and underweight NCD Risk Factor Collaboration (NCD-RisC)

From 1985 to 2016, the prevalence of underweight decreased, and that of obesity and severe obesity increased, in most regions, with significant variation in the magnitude of these changes across regions. We investigated how much change in mean body mass index (BMI) explains changes in the prevalence of underweight, obesity, and severe obesity in different regions using data from 2896 population-based studies with 187 million participants. Changes in the prevalence of underweight and total obesity, and to a lesser extent severe obesity, are largely driven by shifts in the distribution of BMI, with smaller contributions from changes in the shape of the distribution. In East and Southeast Asia and sub-Saharan Africa, the underweight tail of the BMI distribution was left behind as the distribution shifted. There is a need for policies that address all forms of malnutrition by making healthy foods accessible and affordable, while restricting unhealthy foods through fiscal and regulatory restrictions

Contribución a los métodos de generación de distribuciones multivariantes discretas

En esta tesis se propone una metodología sistemática para la generación y estudio de distribuciones de probabilidad multivariantes, basada en la extensión de los sistemas de ecuaciones en diferencias finitas de pearson, ord, kemp, etc.. se generan distribuciones asociadas a funciones hipergeometricas generalizadas bivariantes y multivariantes en general. Se obtienen clasificaciones en función de las características de los parámetros, las cuales extienden otras clasificaciones previas (stein; kemp; ord y van uwen; etc.). Se hace un estudio especial de la distribución generalizada de waring, estudiada por irwing y xecalaki (1983;1984;1986), extendiéndola al caso multivariante, y obteniendo resultados sobre las leyes marginales y condicionadas, así como la estimación vía el método de los momentos; todo ello como ejemplo, por otra parte, de la metodología establecida en esta tesisTesis Universidad de Granada. Departamento de Estadística e Investigación Operativ

Finite Mixture Models in the Evaluation of Positional Accuracy of Geospatial Data

Digital elevation models (DEMs) are highly relevant geospatial products, and their positional accuracy has demonstrated influence on elevation derivatives (e.g., slope, aspect, curvature, etc.) and GIS results (e.g., drainage network and watershed delineation, etc.). The accuracy assessment of the DEMs is usually based on analyzing the altimetric component by means of positional accuracy assessment methods that are based on the use of a normal distribution for error modeling but, unfortunately, the observed distribution of the altimetric errors is not always normal. This paper proposes the application of a finite mixture model (FMM) to model altimetric errors. The way to adjust the FMM is provided. Moreover, the behavior under sampling is analyzed when applying different positional accuracy assessment standards such as National Map Accuracy Standards (NMAS), Engineering Map Accuracy Standard (EMAS) and National Standard for Spatial Data Accuracy (NSSDA) under the consideration of the FMM and the traditional approach-based one-single normal distribution model (1NDM). For the NMAS, the FMM performs statistically much better than the 1NDM when considering all the tolerance values and sample sizes. For the EMAS, the type I error level is around 3.5 times higher in the case of the 1NDM than in the case of the FMM. In the case of the NSSDA, as it has been applied in this research (simple comparison of values, not hypothesis testing), there is no great difference in behavior. The conclusions are clear; the FMM offers results that are always more consistent with the real distribution of errors, and with the supposed statistical behavior of the positional accuracy assessment standard when based on hypothesis testing

Finite Mixture Models in the Evaluation of Positional Accuracy of Geospatial Data

Digital elevation models (DEMs) are highly relevant geospatial products, and their positional accuracy has demonstrated influence on elevation derivatives (e.g., slope, aspect, curvature, etc.) and GIS results (e.g., drainage network and watershed delineation, etc.). The accuracy assessment of the DEMs is usually based on analyzing the altimetric component by means of positional accuracy assessment methods that are based on the use of a normal distribution for error modeling but, unfortunately, the observed distribution of the altimetric errors is not always normal. This paper proposes the application of a finite mixture model (FMM) to model altimetric errors. The way to adjust the FMM is provided. Moreover, the behavior under sampling is analyzed when applying different positional accuracy assessment standards such as National Map Accuracy Standards (NMAS), Engineering Map Accuracy Standard (EMAS) and National Standard for Spatial Data Accuracy (NSSDA) under the consideration of the FMM and the traditional approach-based one-single normal distribution model (1NDM). For the NMAS, the FMM performs statistically much better than the 1NDM when considering all the tolerance values and sample sizes. For the EMAS, the type I error level is around 3.5 times higher in the case of the 1NDM than in the case of the FMM. In the case of the NSSDA, as it has been applied in this research (simple comparison of values, not hypothesis testing), there is no great difference in behavior. The conclusions are clear; the FMM offers results that are always more consistent with the real distribution of errors, and with the supposed statistical behavior of the positional accuracy assessment standard when based on hypothesis testing

Implementación del cálculo de polinomios zonales y aplicaciones en análisis multivariante

En este trabajo se describe la implementación de un algoritmo para el cálculo de polinomios zonales, así como dos aplicaciones explícitas de éstos en el ámbito del análisis multivariante. Concretamente, esta implementación permite obtener resultados de sumación aproximados para funciones hipergeométricas de argumento matricial que, a su vez, pueden utilizarse en la génesis de distribuciones multivariantes discretas con frecuencias simétricas. De igual forma, se pone en práctica un conocido resultado teórico que caracteriza la distribución de la menor raíz característica de una matriz aleatoria con distribución de Wishar

cpd: An R Package for Complex Pearson Distributions

The complex Pearson (CP) distributions are a family of probability models for count data generated by the Gaussian hypergeometric function with complex arguments. The complex triparametric Pearson (CTP) distribution and its biparametric versions, the complex biparametric Pearson (CBP) and the extended biparametric Waring (EBW) distributions, belong to this family. They all have explicit expressions of the probability mass function (pmf), probability generating function and moments, so they are easy to handle from a computational point of view. Moreover, the CTP and EBW distributions can model over- and underdispersed count data, whereas the CBP can only handle overdispersed data, but unlike other well-known overdispersed distributions, the overdispersion is not due to an excess of zeros but other low values of the variable. Finally, the EBW distribution allows the variance to be split into three uniquely identifiable components: randomness, liability and proneness. These properties make the CP distributions of interest in the modeling of a great variety of data. For this reason, and for trying to spread their use, we have implemented an R package called cpd that contains the pmf, distribution function, quantile function and random generation for these distributions. In addition, the package contains fitting functions according to the maximum likelihood. This package is available from the Comprehensive R Archive Network (CRAN). In this work, we describe all the functions included in the cpd package, and we illustrate their usage with several examples. Moreover, the release of a plugin in order to use the package from the interface R Commander tries to contribute to the spreading of these models among non-advanced users

cpd: An R Package for Complex Pearson Distributions

The complex Pearson (CP) distributions are a family of probability models for count data generated by the Gaussian hypergeometric function with complex arguments. The complex triparametric Pearson (CTP) distribution and its biparametric versions, the complex biparametric Pearson (CBP) and the extended biparametric Waring (EBW) distributions, belong to this family. They all have explicit expressions of the probability mass function (pmf), probability generating function and moments, so they are easy to handle from a computational point of view. Moreover, the CTP and EBW distributions can model over- and underdispersed count data, whereas the CBP can only handle overdispersed data, but unlike other well-known overdispersed distributions, the overdispersion is not due to an excess of zeros but other low values of the variable. Finally, the EBW distribution allows the variance to be split into three uniquely identifiable components: randomness, liability and proneness. These properties make the CP distributions of interest in the modeling of a great variety of data. For this reason, and for trying to spread their use, we have implemented an R package called cpd that contains the pmf, distribution function, quantile function and random generation for these distributions. In addition, the package contains fitting functions according to the maximum likelihood. This package is available from the Comprehensive R Archive Network (CRAN). In this work, we describe all the functions included in the cpd package, and we illustrate their usage with several examples. Moreover, the release of a plugin in order to use the package from the interface R Commander tries to contribute to the spreading of these models among non-advanced users

Implementación del càlculo de polinomios zonales y aplicaciones en análisis multivariante

En este trabajo se describe la implementación de un algoritmo para el cálculo de polinomios zonales, así como dos aplicaciones explícitas de éstos en el ámbito del análisis multivariante. Concretamente, esta implementación permite obtener resultados de sumación aproximados para funciones hipergeométricas de argumento matricial que, a su vez, pueden utilizarse en la génesis de distribuciones multivariantes discretas con frecuencias simétricas. De igual forma, se pone en práctica un conocido resultado teórico que caracteriza la distribución de la menor raíz característica de una matriz aleatoria con distribución de Wishart