Some recent developments on complex multivariate distributions

AbstractIn this paper, the author gives a review of the literature on complex multivariate distributions. Some new results on these distributions are also given. Finally, the author discusses the applications of the complex multivariate distributions in the area of the inference on multiple time series

Limiting behavior of the eigenvalues of a multivariate F matrix

AbstractThe spectral distribution of a central multivariate F matrix is shown to tend to a limit distribution in probability under certain conditions as the number of variables and the degrees of freedom tend to infinity

Derivative moments for characteristic polynomials from the CUE

We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried out for finite matrix size and in the limit as the size of the matrices goes to infinity. The latter asymptotic calculation allows us to prove a long-standing conjecture from random matrix theory.Comment: 31 pages, 3 figure

Self-emulsifying therapeutic system: a potential approach for delivery of lipophilic drugs

Self-emulsifying therapeutic system (SETs) provide an effective and intelligent solution to the various issues related to the formulation of hydrophobic drugs with limited solubility in gastrointestinal fluid. Although the potential utility of SETs is well known, only in recent years has a mechanistic understanding of the impact of these systems on drug disposition emerged. These in situ emulsion-forming systems have a high stability when incorporated in various dosage forms. SETs are being looked upon as systems which can overcome the problems associated with delivery of poorly water soluble drugs. An in-depth knowledge about lipids and surfactants that can contribute to these systems, criterion for their selection and the proportion in which they can be used, represent some crucial factors determining the in vivo performance of these systems. This article presents a comprehensive account of various types of self-emulsifying formulations with emphasis on their composition and examples of currently marketed preparations.O sistema terapêutico auto-emulsionante (SETs) fornece solução eficaz e inteligente para os vários problemas relativos à formulação de fármacos hidrofóbicos com solubilidade limitada no fluido gastrintestinal. Embora a utilidade potencial dos SETs seja bem conhecida, só recentemente se compreendeu, mecanisticamente,o impacto desses sistemas na disposição de fármacos. Estes sistemas de formação de emulsão in situ têm alta estabilidade, quando incorporados em várias formas de dosagem. Os SETs têm sido considerados como sistemas que podem resolver problemas associados à liberação de fármacos pouco solúveis em água. O conhecimento profundo dos lipídios e tensoativos que podem ser utilizados para estes sistemas e o critério para a sua seleção e proporção na qual eles são utilizados são alguns dos fatores cruciais que determinam o desempenho do sistema in vivo. Este artigo apresenta o relato abrangente de vários tipos de formulações auto-emulsificantes, com ênfase em sua composição e exemplos das preparações que são correntemente comercializadas

Estimation of multivariate binary density using orthogonal functions

AbstractIn this paper, the authors studied certain properties of the estimate of Liang and Krishnaiah (1985, J. Multivariate Anal. 16, 162–172) for multivariate binary density. An alternative shrinkage estimate is also obtained. The above results are generalized to general orthonormal systems

A structure theorem on bivariate positive quadrant dependent distributions and tests for independence in two-way contingency tables

In this paper, the set of all bivariate positive quadrant dependent distributions with fixed marginals is shown to be compact and convex. Extreme points of this convex set are enumerated in some specific examples. Applications are given in testing the hypothesis of independence against strict positive quadrant dependence in the context of ordinal contingency tables. The performance of two tests, one of which is based on eigenvalues of a random matrix, is compared. Various procedures based upon certain functions of the eigenvalues of a random matrix are also proposed for testing for independence in a two-way contingency table when the marginals are random.asymptotic distributions compact set contingency tables convex set eigenvalues extreme points gamma ratio hypothesis of independence positive quadrant dependent distributions power function