共查询到20条相似文献,搜索用时 11 毫秒
1.
Hyoung-Moon KimMarc G. Genton 《Journal of multivariate analysis》2011,102(7):1105-1117
We obtain the characteristic function of scale mixtures of skew-normal distributions both in the univariate and multivariate cases. The derivation uses the simple stochastic relationship between skew-normal distributions and scale mixtures of skew-normal distributions. In particular, we describe the characteristic function of skew-normal, skew-t, and other related distributions. 相似文献
2.
Given a random sample from a continuous variable, it is observed that the copula linking any pair of order statistics is independent of the parent distribution. To compare the degree of association between two such pairs of ordered random variables, a notion of relative monotone regression dependence (or stochastic increasingness) is considered. Using this concept, it is proved that for i<j, the dependence of the jth order statistic on the ith order statistic decreases as i and j draw apart. This extends earlier results of Tukey (Ann. Math. Statist. 29 (1958) 588) and Kim and David (J. Statist. Plann. Inference 24 (1990) 363). The effect of the sample size on this type of dependence is also investigated, and an explicit expression is given for the population value of Kendall's coefficient of concordance between two arbitrary order statistics of a random sample. 相似文献
3.
Hsiaw-Chan Yeh 《Journal of multivariate analysis》2010,101(4):893-908
Three new multivariate semi-logistic distributions (denoted by MSL(1), MSL(2), and GMSL respectively) are studied in this paper. They are more general than Gumbel’s (1961) [1] and Arnold’s (1992) [2] multivariate logistic distributions. They may serve as competitors to these commonly used multivariate logistic distributions. Various characterization theorems via geometric maximization and geometric minimization procedures of the three MSL(1), MSL(2) and GMSL are proved. The particular multivariate logistic distribution used in the multiple logistic regression model is introduced. Its characterization theorem is also studied. Finally, some further research work on these MSL is also presented. Some probability density plots and contours of the bivariate MSL(1), MSL(2) as well as Gumbel’s and Arnold’s bivariate logistic distributions are presented in the Appendix. 相似文献
4.
Let A(t) be a complex Wishart process defined in terms of the M×N complex Gaussian matrix X(t) by A(t)=X(t)X(t)H. The covariance matrix of the columns of X(t) is Σ. If X(t), the underlying Gaussian process, is a correlated process over time, then we have dependence between samples of the Wishart process. In this paper, we study the joint statistics of the Wishart process at two points in time, t1, t2, where t1<t2. In particular, we derive the following results: the joint density of the elements of A(t1), A(t2), the joint density of the eigenvalues of Σ-1A(t1),Σ-1A(t2), the characteristic function of the elements of A(t1), A(t2), the characteristic function of the eigenvalues of Σ-1A(t1),Σ-1A(t2). In addition, we give the characteristic functions of the eigenvalues of a central and non-central complex Wishart, and some applications of the results in statistics, engineering and information theory are outlined. 相似文献
5.
Subir Kumar Bhandari 《Journal of multivariate analysis》2006,97(6):1355-1360
The celebrated U-conjecture states that under the Nn(0,In) distribution of the random vector X=(X1,…,Xn) in Rn, two polynomials P(X) and Q(X) are unlinkable if they are independent [see Kagan et al., Characterization Problems in Mathematical Statistics, Wiley, New York, 1973]. Some results have been established in this direction, although the original conjecture is yet to be proved in generality. Here, we demonstrate that the conjecture is true in an important special case of the above, where P and Q are convex nonnegative polynomials with P(0)=0. 相似文献
6.
Conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations. Spectral results are also obtained. Several important random walks are now realized this way: Stanley's QS-distribution results from endomorphisms given by evaluation maps, a-shuffles result from the ath convolution power of the universal character, and the Tchebyshev operator of the second kind introduced recently by Ehrenborg and Readdy yields traditional riffle shuffles. A conjecture of Ehrenborg regarding the spectra for a family of random walks on ab-words is proven. A theorem of Stembridge from the theory of enriched P-partitions is also recovered as a special case. 相似文献
7.
A. Plikusas 《Acta Appl Math》1995,38(1):97-107
The central limit theorem and the theorem on large deviations for the functionals of the Poisson random process are proved. The formulas for cumulants of multiple stochastic integrals (m.s.i.) with respect to the Poisson process are obtained. The m.s.i. may be considered as anU-statistics arising in queueing theory as well as a generalization of the well-known Poisson shot-noise process, having wide applications. 相似文献
8.
Hsiaw-Chan Yeh 《Statistics & probability letters》2011,81(9):1370-1379
An autoregressive multivariate stochastic model is constructed which yields a stationary Markov process with a marginal invariant distribution as a multivariate semi-logistic distribution. This model is denoted as an MSL-AR(1) process. Some properties of the MSL-AR(1) process are studied and its characterization is also derived. 相似文献
9.
In this paper, we introduce a new copula-based dependence order to compare the relative degree of dependence between two pairs of random variables. Relationship of the new order to the existing dependence orders is investigated. In particular, the new ordering is stronger than the partial ordering, more monotone regression dependence as developed by Avérous et al. [J. Avérous, C. Genest, S.C. Kochar, On dependence structure of order statistics, Journal of Multivariate Analysis 94 (2005) 159-171]. Applications of this partial order to order statistics, k-record values and frailty models are given. 相似文献
10.
Mihai Putinar 《Archiv der Mathematik》2006,87(1):41-51
We compare three levels of algebraic certificates for evaluating the maximum modulus of a complex analytic polynomial, on
a compact semi-algebraic set. They are obtained as translations of some recently discovered inequalities in operator theory.
Although they can be stated in purely algebraic terms, the only known proofs for these decompositions have a transcendental
character.
Received: 27 June 2005 相似文献
11.
In recent years, the skew-normal models introduced by Azzalini (1985) [1]-and their multivariate generalizations from Azzalini and Dalla Valle (1996) [4]-have enjoyed an amazing success, although an important literature has reported that they exhibit, in the vicinity of symmetry, singular Fisher information matrices and stationary points in the profile log-likelihood function for skewness, with the usual unpleasant consequences for inference. It has been shown (DiCiccio and Monti (2004) [23], DiCiccio and Monti (2009) [24] and Gómez et al. (2007) [25]) that these singularities, in some specific parametric extensions of skew-normal models (such as the classes of skew-t or skew-exponential power distributions), appear at skew-normal distributions only. Yet, an important question remains open: in broader semiparametric models of skewed distributions (such as the general skew-symmetric and skew-elliptical ones), which symmetric kernels lead to such singularities? The present paper provides an answer to this question. In very general (possibly multivariate) skew-symmetric models, we characterize, for each possible value of the rank of Fisher information matrices, the class of symmetric kernels achieving the corresponding rank. Our results show that, for strictly multivariate skew-symmetric models, not only Gaussian kernels yield singular Fisher information matrices. In contrast, we prove that systematic stationary points in the profile log-likelihood functions are obtained for (multi)normal kernels only. Finally, we also discuss the implications of such singularities on inference. 相似文献
12.
J. S. Huang 《Annals of the Institute of Statistical Mathematics》1981,33(1):131-134
For two independent nonnegative random variablesX andY we say thatX is ageless relative toY if the conditional probability P[X> Y+x|X>Y] is defined and is equal to P[X>x] for allx>0. Suppose thatX is ageless relative to a nonlatticeY with P[Y=0]<P [Y<X]. We show that the only suchX is the exponential variable. As a corollary it follows that exponential variable is the only one which possesses the ageless
property relative to a continuous variable.
Research partially supported by NRC of Canada grants #A8057 and #T0500.
Work partially completed while on leave at Division of Math. Stat., C.S.I.R.O., Australia. 相似文献
13.
Roger B. Nelsen José Antonio Rodríguez-Lallena 《Insurance: Mathematics and Economics》2008,42(2):473-483
We study a method, which we call a copula (or quasi-copula) diagonal splice, for creating new functions by joining portions of two copulas (or quasi-copulas) with a common diagonal section. The diagonal splice of two quasi-copulas is always a quasi-copula, and we find a necessary and sufficient condition for the diagonal splice of two copulas to be a copula. Applications of this method include the construction of absolutely continuous asymmetric copulas with a prescribed diagonal section, and determining the best-possible upper bound on the set of copulas with a particular type of diagonal section. Several examples illustrate our results. 相似文献
14.
Christian Genest Subhash C. Kochar Maochao Xu 《Journal of multivariate analysis》2009,100(8):1587-1592
Let Rn be the range of a random sample X1,…,Xn of exponential random variables with hazard rate λ. Let Sn be the range of another collection Y1,…,Yn of mutually independent exponential random variables with hazard rates λ1,…,λn whose average is λ. Finally, let r and s denote the reversed hazard rates of Rn and Sn, respectively. It is shown here that the mapping t?s(t)/r(t) is increasing on (0,∞) and that as a result, Rn=X(n)−X(1) is smaller than Sn=Y(n)−Y(1) in the likelihood ratio ordering as well as in the dispersive ordering. As a further consequence of this fact, X(n) is seen to be more stochastically increasing in X(1) than Y(n) is in Y(1). In other words, the pair (X(1),X(n)) is more dependent than the pair (Y(1),Y(n)) in the monotone regression dependence ordering. The latter finding extends readily to the more general context where X1,…,Xn form a random sample from a continuous distribution while Y1,…,Yn are mutually independent lifetimes with proportional hazard rates. 相似文献
15.
Ivan ?e?ula 《Journal of multivariate analysis》2006,97(3):606-618
Standard and extended growth curve model (multivariate linear model) with practically important variance structures are considered and a method for parameters estimation is proposed. 相似文献
16.
S. DelattreE. Roquain 《Statistics & probability letters》2011,81(1):111-115
We study the convergence of the false discovery proportion (FDP) of the Benjamini-Hochberg procedure in the Gaussian equi-correlated model, when the correlation ρm converges to zero as the hypothesis number m grows to infinity. In this model, the FDP converges to the false discovery rate (FDR) at rate {min(m,1/ρm)}1/2, which is different from the standard convergence rate m1/2 holding under independence. 相似文献
17.
18.
Situations occur frequently in which the mean residual life (mrl) functions of two populations must be ordered. For example, if a mechanical device is improved, the mrl function for the improved device should not be less than that of the original device. Also, mrl functions for medical patients should often be ordered depending on the status of concomitant variables. This paper proposes nonparametric estimators of the bivariate mrl function under a mrl ordering. The estimators are shown to be asymptotically unbiased, strongly uniformly consistent and weakly convergent to a bivariate Gaussian process. The estimators are shown to be the projections, in a sense to be made precise, of the empirical mrl function onto an appropriate convex set of mrl functions. In the one-sample problem, the new estimators dominate the empirical mrl function in terms of risk with respect to a wide class of loss functions. 相似文献
19.
Let X1,…,Xn be a random sample from an absolutely continuous distribution with non-negative support, and let Y1,…,Yn be mutually independent lifetimes with proportional hazard rates. Let also X(1)<?<X(n) and Y(1)<?<Y(n) be their associated order statistics. It is shown that the pair (X(1),X(n)) is then more dependent than the pair (Y(1),Y(n)), in the sense of the right-tail increasing ordering of Avérous and Dortet-Bernadet [LTD and RTI dependence orderings, Canad. J. Statist. 28 (2000) 151-157]. Elementary consequences of this fact are highlighted. 相似文献
20.
Motivated by the likelihood functions of several incomplete categorical data, this article introduces a new family of distributions, grouped Dirichlet distributions (GDD), which includes the classical Dirichlet distribution (DD) as a special case. First, we develop distribution theory for the GDD in its own right. Second, we use this expanded family as a new tool for statistical analysis of incomplete categorical data. Starting with a GDD with two partitions, we derive its stochastic representation that provides a simple procedure for simulation. Other properties such as mixed moments, mode, marginal and conditional distributions are also derived. The general GDD with more than two partitions is considered in a parallel manner. Three data sets from a case-control study, a leprosy survey, and a neurological study are used to illustrate how the GDD can be used as a new tool for analyzing incomplete categorical data. Our approach based on GDD has at least two advantages over the commonly used approach based on the DD in both frequentist and conjugate Bayesian inference: (a) in some cases, both the maximum likelihood and Bayes estimates have closed-form expressions in the new approach, but not so when they are based on the commonly-used approach; and (b) even if a closed-form solution is not available, the EM and data augmentation algorithms in the new approach converge much faster than in the commonly-used approach. 相似文献