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## Beta-binomial/Poisson regression models for repeated bivariate counts

LORA, Mayra Ivanoff; SINGER, Julio M.
Fonte: JOHN WILEY & SONS LTD Publicador: JOHN WILEY & SONS LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
35.96%
We analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of Parkinson`s disease patients. Maximum likelihood methods were used to fit beta-binomial/Poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods, controlling for disease stage and use of the preferred hand. We extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data. The results suggest that the expected number of attempts and successes increase with training, except for patients with advanced stages of the disease using the non-preferred hand. Copyright (c) 2008 John Wiley & Sons, Ltd.

## The Kumaraswamy Gumbel distribution

Cordeiro, Gauss M.; Nadarajah, Saralees; Ortega, Edwin M. M.
Fonte: SPRINGER HEIDELBERG; HEIDELBERG Publicador: SPRINGER HEIDELBERG; HEIDELBERG
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
45.9%
The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose a generalization-referred to as the Kumaraswamy Gumbel distribution-and provide a comprehensive treatment of its structural properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters. We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality of the proposed model. Two bivariate generalizations of the model are proposed.

## Modelos Beta-Binomial/Poisson-Gama para contagens bivariadas repetidas; Beta-binomial/gamma-Poisson regression models for repeated bivariate counts

Lora, Mayra Ivanoff
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
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Em Lora e Singer (Statistics in Medicine, 2008), propusemos um modelo Beta- Binomial/Poisson p-variado para análise dos dados provenientes de um estudo que consistiu em contar o número de tentativas e acertos de um exercício manual com duração de um minuto realizado por doentes de Parkinson, antes e depois de um treinamento. O objetivo era verificar se o treinamento aumentava o número de tentativas e a porcentagem de acerto, o que destaca o aspecto bivariado do problema. Esse modelo leva tais características em consideração, usa uma distribuição adequada para dados de contagem e ainda acomoda a sobredispersão presente na contagem dos acertos. Como generalização, inicialmente, propomos um modelo Beta-Binomial/Poisson-Gama que acomoda sobredispersão também para as contagens dos totais de tentativas, além incluir covariâncias possivelmente diferentes entre as contagens em diversos instantes de avaliação. Neste novo modelo, introduzimos um parâmetro que relaciona o total de tentativas com a probabilidade de acerto, tornando-o ainda mais geral. Obtemos estimadores de máxima verossimilhança dos parâmetros utilizando um algoritmo de Newton-Raphson. Consideramos um outro conjunto de dados provenientes do mesmo estudo para ilustração da metodologia proposta.; In Lora and Singer (Statistics in Medicine...

## Modelos de regressão beta-binomial/poisson para contagens bivariadas; Beta-binomial/Poisson regression models for repeated bivariate counts

Lora, Mayra Ivanoff
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
36.1%
Propomos um modelo Beta-Binomial/Poisson para dados provenientes de um estudo com doentes de Parkinson, que consistiu em contar durante um minuto quantas tarefas foram realizadas e destas, quantas de maneira correta, antes e depois de um treinamento. O objetivo era verificar se o treinamento aumentava o número de tentativas e a porcentagem de acerto, o que destaca o aspecto bivariado do problema. Esse modelo considera tal aspecto, usa uma distribuição mais adequada a dados de contagem e ainda suporta a sobredispersão presente nos dados. Obtemos estimadores de máxima verossimilhança dos parâmetros utilizando um algoritmo de Newton-Raphson. Ilustramos a aplicação da metodologia desenvolvida aos dados do estudo.; We propose a Beta-Binomial/Poisson model to the data from a study with Parkinson disease patients, which consisted in counting for one minute how many trials were attempted and how many of them were successful, before and after a training period. The main goal was to check if training increased the number of trials and success probability, which emphasizes the bivariate aspect of the problem. This model takes this aspect into account, uses a distribution which is usually more adequate to count data and supports the overdispersion present in the data. We obtain the maximum likelihood estimators using a Newton-Raphson algorithm. For illustration...

## On measures of association among genetic variables

Gianola, Daniel; Manfredi, Eduardo; Simianer, Henner
Fonte: Blackwell Publishing Ltd Publicador: Blackwell Publishing Ltd
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
26.01%
Systems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. New measures of association based on notions of statistical distance between distributions are presented. These are more general than correlations, which are pairwise measures, and lack a clear interpretation beyond the bivariate normal distribution. Our measures are based on logarithmic (Kullback-Leibler) and on relative ‘distances’ between distributions. Indexes of association are developed and illustrated for quantitative genetics settings in which the joint distribution of the variables is either multivariate normal or multivariate-t, and we show how the indexes can be used to study linkage disequilibrium in a two-locus system with multiple alleles and present applications to systems of correlated beta distributions. Two multivariate beta and multivariate beta-binomial processes are examined, and new distributions are introduced: the GMS-Sarmanov multivariate beta and its beta-binomial counterpart.

## Propriedades das distribuições bivariadas de crovelli, gumbel tipo I e gama beta tipo II, com uma aplicação a dados de precipitação pluviométrica; Properties of crovelli´s bivariate gamma distribution, gumbel type I and gamma beta type II, with an application to rainfall data

Fonte: UNIVERSIDADE FEDERAL DE LAVRAS; DEX - Departamento de Ciências Exatas; UFLA; BRASIL Publicador: UNIVERSIDADE FEDERAL DE LAVRAS; DEX - Departamento de Ciências Exatas; UFLA; BRASIL
PT_BR
Relevância na Pesquisa
36.1%

## A Note on the Characterization of Bivariate Densities by Conditional Densities

Abrahams, Julia; Thomas, John B.; Abrahams, Julia; Thomas, John B.
Tipo: Relatório
ENG
Relevância na Pesquisa
35.95%
Tech Report; The compatibility of pairs of conditional densities and the uniqueness of the resulting bivariate densities are discussed. Examples are given involving beta, gamma, and Gaussian conditional densities.

## An autoregressive process for Beta random variables

McKenzie, Edward
Tipo: Relatório
EN_US
Relevância na Pesquisa
36.12%
Two stationary first-order autoregressive processes with Beta marginal distributions are presented. They are both linear, additive processes but the coefficients are Beta random variables. Their autocorrelation functions are investigated: One is positive and the other alternates in sign. The usefulness of the models in simulatino is discussed. The Bivariate Beta distributions are two consecutive observations are considered in some detail. Several examples are given, including a Bivariate Uniform process which is also examined in detail. The relationship of these Bivariate Beta distributions to the Dirichelet distribution is discussed.

## A Bootstrap Likelihood approach to Bayesian Computation

Zhu, Weixuan; Marín Diazaraque, Juan Miguel; Leisen, Fabrizio
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper
Relevância na Pesquisa
66.06%
Recently, an increasingly amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. These algorithms are known as Approximate Bayesian Computational (ABC) methods. One of the problems of these algorithms is that the performance depends on the tuning of some parameters, such as the summary statistics, distance and tolerance level. To bypass this problem, an alternative method based on empirical likelihood was introduced by Mengersen et al. (2013), which can be easily implemented when a set of constraints, related with the moments of the distribution, is known. However, the choice of the constraints is crucial and sometimes challenging in the sense that it determines the convergence property of the empirical likelihood. To overcome this problem, we propose an alternative method based on a bootstrap likelihood approach. The method is easy to implement and in some cases it is faster than the other approaches. The performance of the algorithm is illustrated with examples in Population Genetics, Time Series and a recent non-explicit bivariate Beta distribution. Finally, we test the method on simulated and real data random fields.

## Common Patterns of Energy Flow and Biomass Distribution on Weighted Food Webs

Zhang, Jiang; Feng, Yuanjing
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.89%
Weights of edges and nodes on food webs which are available from the empirical data hide much information about energy flows and biomass distributions in ecosystem. We define a set of variables related to weights for each species $i$, including the throughflow $T_i$, the total biomass $X_i$, and the dissipated flow $D_i$ (output to the environment) to uncover the following common patterns in 19 empirical weighted food webs: (1) DGBD distributions (Discrete version of a Generalized Beta Distribution), a kind of deformed Zipf's law, of energy flow and storage biomass; (2) The allometric scaling law $T_i\propto X_i^{\alpha}$, which can be viewed as the counterpart of the Kleiber's 3/4 law at the population level; (3) The dissipation law $D_i\propto T_i^{\beta}$; and (4) The gravity law, including univariate version $f_{ij}\propto (T_iT_j)^{\gamma}$ and bivariate approvement $f_{ij}\propto T_i^{\gamma_1}T_j^{\gamma_2}$. These patterns are very common and significant in all collected webs, as a result, some remarkable regularities are hidden in weights.; Comment: 26 pages, 7 figures

## Spectral distribution method for neutrinoless double-beta decay nuclear transition matrix elements: Binary correlation results

Vyas, Manan; Kota, V. K. B.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.06%
Neutrinoless double-beta decay nuclear transition matrix elements are generated by an effective two-body transition operator and it consists of Gamow-Teller like and Fermi like (also tensor) operators. Spectral distribution method for the corresponding transition strengths (squares of the transition matrix elements) involves convolution of the transition strength density generated by the non-interacting particle part of the Hamiltonian with a spreading function generated by the two-body part of the Hamiltonian. Extending the binary correlation theory for spinless embedded $k$-body ensembles to ensembles with proton-neutron degrees of freedom, we establish that the spreading function is a bivariate Gaussian for transition operators $\co(k_\co)$ that change $k_\co$ number of neutrons to $k_\co$ number of protons. Towards this end, we have derived the formulas for the fourth-order cumulants of the spreading function and calculated their values for some heavy nuclei; they are found to vary from $\sim -0.4$ to -0.1. Also for nuclei from $^{76}$Ge to $^{238}$U, the bivariate correlation coefficient is found to vary from $\sim 0.6 - 0.8$ and these values can be used as a starting point for calculating nuclear transition matrix elements using the spectral distribution method.; Comment: 28 pages...

## Constructions for a bivariate beta distribution

Olkin, Ingram; Trikalinos, Thomas A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.26%
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate beta distribution plays a similar role for two probabilities that have a bivariate binomial distribution. We provide a new multivariate distribution with beta marginal distributions, positive probability over the unit square, and correlations over the full range. We discuss its extension to three or more dimensions.; Comment: 10 pages, 1 table, 1 figure

## Complex bimatrix variate generalised beta distributions

Diaz-Garcia, Jose A.; Gutierrez-Jaimez, Ramon
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.87%
In this paper, the study of bivariate generalised beta type I and II distributions is extended to the complex matrix variate case, for which the corresponding density functions are found. In addition, for complex bimatrix variate beta type I distributions, several basic properties, including the joint eigenvalue density and the maximum eigenvalue distribution, are studied.; Comment: 13 pages

## Distribution and asymptotics under beta random scaling

Hashorva, Enkelejd; Pakes, Anthony
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.97%
Let X,Y,B be three independent random variables such that $X$ has the same distribution function as Y B. Assume that B is a Beta random variable with positive parameters a,b and Y has distribution function H. Pakes and Navarro (2007) show under some mild conditions that the distribution function H_{a,b} of X determines H. Based on that result we derive in this paper a recursive formula for calculation of H, if H_{a,b} is known. Furthermore, we investigate the relation between the tail asymptotic behaviour of X and Y. We present three applications of our asymptotic results concerning the extremes of two random samples with underlying distribution functions H and H_{a,b}, respectively, and the conditional limiting distribution of bivariate elliptical distributions.; Comment: 12 pages

## Bayesian nonparametric modeling for mean residual life regression

Poynor, Valerie; Kottas, Athanasios
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.86%
The mean residual life function is a key functional for a survival distribution. It has practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the survival distribution. However, it has received limited attention in terms of inference methods under a probabilistic modeling framework. In this paper, we seek to provide general inference methodology for mean residual life regression. Survival data often include a set of predictor variables for the survival response distribution, and in many cases it is natural to include the covariates as random variables into the modeling. We thus propose a Dirichlet process mixture modeling approach for the joint stochastic mechanism of the covariates and survival responses. This approach implies a flexible model structure for the mean residual life of the conditional response distribution, allowing general shapes for mean residual life as a function of covariates given a specific time point, as well as a function of time given particular values of the covariate vector. To expand the scope of the modeling framework, we extend the mixture model to incorporate dependence across experimental groups, such as treatment and control groups. This extension is built from a dependent Dirichlet process prior for the group-specific mixing distributions...

## Dependent Indian Buffet Process-based Sparse Nonparametric Nonnegative Matrix Factorization

Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Da Xu, Richard Yi; Luo, Xiangfeng
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.06%
Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices appropriate for the intended applications. The method has been widely used for unsupervised learning tasks, including recommender systems (rating matrix of users by items) and document clustering (weighting matrix of papers by keywords). However, traditional NMF methods typically assume the number of latent factors (i.e., dimensionality of the loading matrices) to be fixed. This assumption makes them inflexible for many applications. In this paper, we propose a nonparametric NMF framework to mitigate this issue by using dependent Indian Buffet Processes (dIBP). In a nutshell, we apply a correlation function for the generation of two stick weights associated with each pair of columns of loading matrices, while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two loading matrices will be column-wise (indirectly) correlated. Under this same framework, two classes of correlation function are proposed (1) using Bivariate beta distribution and (2) using Copula function. Both methods allow us to adopt our work for various applications by flexibly choosing an appropriate parameter settings. Compared with the other state-of-the art approaches in this area...

## Variations in the Bivariate Brightness Distribution with different galaxy types

Cross, Nicholas; Driver, Simon; Lemon, David; Liske, Jochen
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.95%
We present Bivariate Brightness Distributions (BBDs) for four spectral types discriminated by the 2dFGRS. We discuss the photometry and completeness of the 2dFGRS using a deep, wide-field CCD imaging survey. We find that there is a strong luminosity-surface brightness correlation amongst galaxies with medium to strong emission features, with gradient $\beta_{\mu}=0.25\pm0.05$ and width $\sigma_{\mu}=0.56\pm0.01$. Strong absorption line galaxies, show a bimodal distribution, with no correlation between luminosity and surface brightness.; Comment: 4 pages, 2 figures, In the "New Era in Cosmology" conference, Durham, Sept 2001, ASP conference series

## The Bivariate Size-luminosity Relations for Lyman Break Galaxies at z ~ 4 - 5

Huang, Kuang-Han; Ferguson, Henry C.; Ravindranath, Swara; Su, Jian
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.11%
We study the bivariate size-luminosity distribution of Lyman Break Galaxies (LBGs) selected at redshifts around 4 and 5 in GOODS and the HUDF fields. We model the size-luminosity distribution as a combination of log-normal distribution (in size) and Schechter function (in luminosity), therefore it enables a more detailed study of the selection effects. We perform extensive simulations to quantify the dropout-selection completenesses and measurement biases and uncertainties in two-dimensional size and magnitude bins, and transform the theoretical size-luminosity distribution to the expected distribution for the observed data. Using maximum-likelihood estimator (MLE), we find that the Schechter function parameters for B-dropouts are \alpha=-1.68^{+0.068}_{-0.095}, M*=-20.60^{+0.13}_{-0.17}, and \phi*=1.79^{+0.32}_{-0.52} x 10^{-3} Mpc^{-3}. The log-normal size distribution is characterized by the peak R_0=1.34^{+0.099}_{-0.108} kpc at M_{1500}=-21 mag, width \sigma_{\lnR}=0.83^{+0.046}_{-0.044}, and the slope of the size-luminosity (RL) relation \beta=0.22^{+0.058}_{-0.056}. Similarly, for V-dropouts we find \alpha=-1.74^{+0.15}_{-0.20}, M*=-20.53^{+0.24}_{-0.27}, \phi*=1.55^{+0.62}_{-0.77} x 10^{-3} Mpc}^{-3}, R_0=1.19^{+0.21}_{-0.16} kpc...

## Muliere and Scarsini’s bivariate Pareto distribution: sums, products, and ratios

Tipo: Artigo de Revista Científica Formato: application/pdf