| 4/2009 |
On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation R. Figueiredo Camargo, Edmundo Capelas de Oliveira, Jayme Vaz Jr. The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral), equations. The so-called generalized Mittag-Leffler function, a function with three-parameter, which generalizes the classical ones, appear in the fractional telegraph equation. Here we introduce some integral transforms associated with this generalizedMittag-Leffler function. As particular cases some recent results are recovered. |
| 3/2009 |
Classification of Reversible-Equivariant Vector Fields in 4D with Applications to Normal Forms and First Integrals Ricardo M. Martins, Marco A. Teixeira This paper uses tools in group theory and symbolic computing to give a classification of the representations of finite groups with order lower than 9 that can be derived from the study of local reversible-equivariant vector fields in $\rn{4}$. Based on such approach we exhibit, for each element in this class of dynamical systems, a simplified Belitiskii normal form and establish conditions for the existence of first integrals.  rp-2009-3.pdf |
| 2/2009 |
Some Estimators of Molecular Polymorphism and their Asymptotic Behavior Samara F. Kiihl, Hildete P. Pinheiro, Aluísio Pinheiro, Sérgio F. dos Reis Important aspects of population evolution have been investigated using nucleotide sequences. The quantity µ, representing the mean number of mutations per gene per generation, is an essential parameter in population evolution studies, since it determines the degree of polymorphism in a locus. Inferences about the evolution of a population are measured by the accuracy of estimation of this parameter. In this article we present various methods of estimation of µ, analytical studies of their asymptotic distributions as well as comparisons of the distribution’s behavior of these estimators through simulations. rp-2009-2.pdf |
| 1/2009 |
On the Fractional Langevin Equations R. Figueiredo Camargo, Ary O. Chiacchio, Reinaldo Charnet, Edmundo Capelas de Oliveira We present and discuss a fractional version of the Langevin differintegral equation as a generalization of the standard Langevin equation. Some particular cases are presented. |
| 29/2008 |
On Some Fractional Green´s Functions R. Figueiredo Camargo, Reinaldo Charnet, Edmundo Capelas de Oliveira In this paper we discuss some fractional Green's functions associated with the fractional differential equations which appear in several fields of science, more precisely, the so-called wave reaction-diffusion equation and some of its particular cases. The methodology presented is the juxtaposition of integral transforms, in particular, the Laplace and the Fourier integral transforms. Some recent results involving the reaction-diffusion equation are pointed out. |
| 28/2008 |
Optimal Cubature Formulas on Compact Homogeneous Manifolds Alexander Kushpel We find lower bounds for the rate of convergence of optimal cubature formulas on sets of differentiable functions on compact homogeneous manifolds of rank I or two-point homogeneous spaces. It is shown that these lower bounds are sharp in the power scale in the case of $\mathbb{S}^{2}$, the unit sphere in $\mathbb{R}^{3}$. |
| 27/2008 |
Robust Bayesian Analysis of Heavy-tailed Stochastic Volatility Models using Scale Mixtures of Normal Distributions Carlos A. Abanto-Valle, D. Bandyopadhyay, Víctor H. Lachos, I. Enriquez This paper consider a Bayesian analysis of stochastic volatility models using a class of symmetric normal scale mixtures, which provides an appealing robust alternative to the routine use of the normal distribution in this type of models. Specific distributions examined include the normal, the Student-t, the slash and the variance gamma distribution which are obtained as a sub-class of our proposed class of models. Under a Bayesian paradigm, we explore an efficient Markov chain Monte Carlo (MCMC) algorithm for parameter estimation in this model. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify possible outliers. The methods developed are applied to analyze daily stock returns data on S\&P500 index. We conclude that our proposed rich class of normal scale mixture models provides an interesting robust alternative to the traditional normality assumptions often used to model thick-tailed stochastic volatility data. rp-2008-27.pdf |
| 26/2008 |
Robust Linear Mixed Models with Skew-Normal Independent Distributions from a Bayesian Perspective Víctor H. Lachos, Dipak K. Dey, Vicente G. Cancho Linear mixed models were developed to handle clustered data and have been a topic of increasing interest in statistics for the past fifty years. Generally, the normality (or symmetry) of the randomeffects is a common assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize skew-normal/independent distributions as a tool for robust modeling of linear mixed models under a Bayesian paradigm. The skew-normal/independent distributions is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal distribution, the skew-t distribution, the skew-slash distribution and the skew contaminated normal distribution as special cases, providing an appealing robust alternative to the routine use of symmetric distributions in this type of models. The methods developed are illustrated using a real data set from Framingham cholesterol study. rp-2008-26.pdf |
| 25/2008 |
On Estimation and Local Influence Analysis for Measurement Errors Models under Heavy-tailed Distributions Víctor H. Lachos, T. Angolini, Carlos A. Abanto-Valle Scale mixtures of normal distribution is a class of symmetric thick--tailed distributions that includes the normal one as a special case. In this paper we consider local influence analysis for measurement error model (MEM) when the random error and the unobserved value of the covariates follows jointly a scale mixtures of normal distribution, providing an appealing robust alternative to the usual Gaussian process in measurement error models. As the observed data log-likelihood associated with this model is intractable, Cook's well--known approach may be hard to be applied to obtain measures of local influence. Instead we develop local influence measures following the approach of Zhu and Lee (2001), which is based on the use of an EM-type algorithm. Three specific perturbation schemes are discussed. Results obtained from a real data set are reported, illustrating the usefulness of the proposed methodology. rp-2008-25.pdf |
| 24/2008 |
An Explicit Formula for a Boundary Map Mari Sano We give an explicit formula for the first boundary map of the resolution constructed in [3], by means of writing the aprorpiate map between complexes. rp-2008-24.pdf |
