STRUCTURES OF SYSTEMS WITH EXPONENTIAL LIFE DISTRIBUTIONS

Abstract. Structures of monotone systems and cold standby systems with     

A concept of negative dependence using stochastic ordering

A concept of negative dependence called negative dependence by stochastic ordering is introduced. This concept satisfies various closure properties. It is shown that three models for negetive dependence satisfy it and that it implies the basic negative orthant inequalities. This concept is also satisfied by the multinomial, multivariate hypergeometric. Dirichlet and Dirichlet compound multinomial distributions. Furthermore, the joint distribution of ranks of a sample and the multivariate normal with nonpositive pairwise correlations also satisfy this condition. The positive dependence analog of this condition is also studied.     

Monitoring the mean of multivariate financial time series

Timely detection of changes in the mean vector of multivariate financial time series is of great practical importance. In this paper, the covariance dynamics of the multivariate stochastic processes is assessed by either the RiskMetrics approach, the constant conditional correlation, or the dynamic conditional correlation models. For online monitoring of mean changes, we introduce several control schemes based on exponential smoothing and cumulative sums, which explicitly account for heteroscedasticity. The detecting ability of the introduced charts is compared for different processes in a Monte Carlo simulation study. The empirical study illustrates monitoring of changes in the mean vector of daily returns of exchange rates. Copyright © 2013 John Wiley & Sons, Ltd.     

A Multivariate CLT for Local Dependence withn log nRate and Applications to Multivariate Graph Related Statistics

This paper concerns the rate of convergence in the central limit theorem for certain local dependence structures. The main goal of the paper is to obtain estimates of the rate in the multidimensional case. Certain one-dimensional results are also improved by using some more flexible characteristics of dependence. Assuming the summands are bounded, we obtain rates close to those for independent variables. As an application we study the rate of the normal approximation of certain graph related statistics which arise in testing equality of several multivariate distributions     

Variational Inequalities for Arbitrary Multivariate Distributions

Upper bounds for the total variation distance between two arbitrary multivariate distributions are obtained in terms of the correspondingw-functions. The results extend some previous inequalities satisfied by the normal distribution. Some examples are also given.     

On a measure of multivariate skewness and a test for multivariate normality

Summary We consider an extension of Pearson measure of skewness to a multivariate case and apply the proposed measure to a test of multivariate normality.     

Some Classes of Multivariate Life Distributions in Discrete Time

New classes of multivariate survival distribution functions based on monotonic behaviour of a multivariate failure rate are developed in the discrete set up. Relationship among the classes along with multivariate geometric distributions that act as boundaries of the various classes are identified.     

Multiparameter estimation for some multivariate discrete distributions with possibly dependent components

Summary In multiparameter estimation for multivariate discrete distributions with infinite support, inadmissibility problems in situations where the multivariate probability distribution function isnot a product of the one-dimensional marginal probability distribution functions have previously been unexplored. This paper examines the inadmissibility problem in some of these situations. Special attention is given to estimating the mean of a negative multinomial distribution. In estimating the mean vector, certain Clevenson-Zidek type estimators are shown to be uniformly better than the usual estimator under a large class of generally scaled squared loss functions. Some of the results are generalized to other multivariate discrete distributions and to situations where several independent negative multinomial distributions are considered.     

On a new multivariate IFR ageing notion based on the standard construction

Many criteria of ageing for random variables or vectors have been proposed in the literature over many years. For instance, a random variable is increasing in failure rate (IFR) if, and only if, it can be ordered with an exponentially distributed random variable in the classical univariate convex transform order. A new multivariate generalization of the convex transform order has recently been proposed in the literature. In this work, we propose a new multivariate IFR notion for multivariate distributions based on comparisons in this new order with a properly defined exponentially distributed random vector. Properties, applications, and illustrations of this new notion are given as well. Copyright © 2016 John Wiley & Sons, Ltd.     

A Complete Characterization of Multivariate Normal Stable Tweedie Models through a Monge-Ampère Property

Extending normal gamma and normal inverse Gaussian models, multivariate normal stable Tweedie (NST) models are composed by a fixed univariate stable Tweedie variable having a positive value domain, and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component. Within the framework of multivariate exponential families, the NST models are recently classified by their covariance matrices V(m) depending on the mean vector m. In this paper, we prove the characterization of all the NST models through their determinants of V(m), also called generalized variance functions, which are power of only one component of m. This result is established under the NST assumptions of Monge-Ampère property and steepness. It completes the two special cases of NST, namely normal Poisson and normal gamma models. As a matter of fact, it provides explicit solutions of particular Monge-Ampère equations in differential geometry.     

基于情景分析的多维拟凸风险统计量

本文定义了三类特殊的多维风险统计量,分别是多维共单调拟凸风险统计量、多维拟凸风险统计量和多维经验分布不变拟凸风险统计量,并采用对偶方法给出了它们的表示定理.本文的结果既是一维拟凸风险统计量的推广,也是多维凸风险统计量的拓展.     

Interpolation from spaces spanned by monomials

This is an extension and emendation of recent results on the use of Gauss elimination in multivariate polynomial interpolation and, in particular, ideal interpolation. Dedicated to Mariano Gasca on the occasion of his sixtieth birthday     

Inferences on interclass and intraclass correlations in multivariate familial data

Inference procedures for interelass and intraclass correlations are given in the multivariate context of familial data for which measurements are taken on more than one characteristic. Unified estimators are proposed based on a certain class of unbiased estimators of covariance matrices. Asymptotic distributions of the proposed estimators are derived under the assumption of multivariate normality. The results can be used to construct approximate confidence intervals and test procedures.Research supported by the Department of Statistics, the Pennsylvania State University and the Air Force Office of Scientific Research under Grant AFSO-88-0030.Institute of Statistical Mathematics     

Some extension of Haldane's multivariate median and its application

Summary Some extension of Haldane's multivariate median is carried out by minimization principle of a specified distance function. Then, making use of the median, three types of measures of multivariate skewness are introduced and their asymptotic null distributions are obtained.     

Multivariate Dispersion Models

We introduce a class of multivariate dispersion models suitable as error distributions for generalized linear models with multivariate non-normal responses. The models preserve some of the main properties of the multivariate normal distribution, and include the elliptically contoured distributions and certain other known distributions as special cases. We give explicit methods for constructing multivariate proper dispersion models. This is exemplified by constructing multivariate gamma, Laplace, hyperbola, and von Mises distributions.     

Multivariate orthogonal polynomials, homogeneous Padé approximants and Gaussian cubature

The connection between orthogonal polynomials, Padé approximants and Gaussian quadrature is well known and will be repeated in section 1. In the past, several generalizations to the multivariate case have been suggested for all three concepts [4,6,9,...], however without reestablishing a fundamental and clear link. In sections 2 and 3 we will elaborate definitions for multivariate Padé and Padé-type approximation, multivariate polynomial orthogonality and multivariate Gaussian integration in order to bridge the gap between these concepts. We will show that the new m-point Gaussian cubature rules allow the exact integration of homogeneous polynomials of degree 2m−1, in any number of variables. A numerical application of the new integration rules can be found in sections 4 and 5. This revised version was published online in June 2006 with corrections to the Cover Date.     

Some extremal properties of multivariate polynomial splines in the metric Lp (Rd )

We constructed a kind of continuous multivariate spline operators as the approximation tools of the multivariate functions on the Bd instead of the usual multivariate cardinal interpolation oper-ators of splines, and obtained the approximation error by this kind of spline operators. Meantime, by the results, we also obtained that the spaces of multivariate polynomial splines are weakly asymptoti-cally optimal for the Kolmogorov widths and the linear widths of some anisotropic Sobolev classes of smooth functions on Bd in the metric Lp(Bd).     

Forecasting mortality rate by multivariate singular spectrum analysis

In this paper, we investigate the possibility of using multivariate singular spectrum analysis (SSA), a nonparametric technique in the field of time series analysis, for mortality forecasting. We consider a real data application with 9 European countries: Belgium, Denmark, Finland, France, Italy, Netherlands, Norway, Sweden, and Switzerland, over a period 1900 to 2009, and a simulation study based on the data set. The results show the superiority of multivariate SSA in comparison with the univariate SSA, in terms of forecasting accuracy.     

Multivariate Vandermonde Determinants and General Birkhoff Interpolation

In this paper, we consider the Straight Line Type Node Configuration C (SLTNCC) in multivariate polynomial interpolation as the result of different kinds of transformations of lines (such as parallel translations, rotations). Corresponding to these transformations we define different kinds of interpolation problems for the SLTNCC. The expression of the confluent multivariate Vandermonde determinant of the coefficient matrix for each of these interpolation problems is obtained, and from this expression we conclude the related interpolation problem is unisolvent. Also, we give a kind of generalization of the SLTNCC in Section 5. As well, we obtain an expression of the interpolating polynomial for a kind of interpolation problem discussed in this paper.     

On generating multivariate Poisson data in management science applications

Generating multivariate Poisson random variables is essential in many applications, such as multi echelon supply chain systems, multi‐item/multi‐period pricing models, accident monitoring systems, etc. Current simulation methods suffer from limitations ranging from computational complexity to restrictions on the structure of the correlation matrix, and therefore are rarely used in management science. Instead, multivariate Poisson data are commonly approximated by either univariate Poisson or multivariate Normal data. However, these approximations are often not adequate in practice. In this paper, we propose a conceptually appealing correction for NORTA (NORmal To Anything) for generating multivariate Poisson data with a flexible correlation structure and rates. NORTA is based on simulating data from a multivariate Normal distribution and converting it into an arbitrary continuous distribution with a specific correlation matrix. We show that our method is both highly accurate and computationally efficient. We also show the managerial advantages of generating multivariate Poisson data over univariate Poisson or multivariate Normal data. Copyright © 2011 John Wiley & Sons, Ltd.