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Paul Embrechts 《Journal of multivariate analysis》2006,97(2):526-547
Li et al. [Distributions with Fixed Marginals and Related Topics, vol. 28, Institute of Mathematics and Statistics, Hayward, CA, 1996, pp. 198-212] provide bounds on the distribution and on the tail for functions of dependent random vectors having fixed multivariate marginals. In this paper, we correct a result stated in the above article and we give improved bounds in the case of the sum of identically distributed random vectors. Moreover, we provide the dependence structures meeting the bounds when the fixed marginals are uniformly distributed on the k-dimensional hypercube. Finally, a definition of a multivariate risk measure is given along with actuarial/financial applications. 相似文献
3.
This paper introduces a new kind of modified transportation cost inequalities and presents some sufficient and necessary conditions for it. Using these conditions, this paper provides some applications of polynomial concentration inequalities to probability measures with no exponential moments. The tensorization property is also provided. 相似文献
4.
Interpolation, correlation identities, and inequalities for infinitely divisible variables 总被引:1,自引:0,他引:1
Christian Houdré Victor Pérez-Abreu Donatas Surgailis 《Journal of Fourier Analysis and Applications》1998,4(6):651-668
We present an interpolation formula for the expectation of functions of infinitely divisible (i.d.) variables. This is then
applied to study the association problem for i.d. vectors and to present new covariance expansions and correlation inequalities.
Acknowledgements and Notes. The research of C. Houdré was supported in part by an NSF Mathematical Sciences Post-Doctoral Fellowship and by an NSF-NATO
Postdoctoral Fellowship and by the NSF grant No. DMS-98032039. This research was completed while V. Pérez-Abreu was visiting
the Georgia Institute of Technology. 相似文献
5.
A permanental vector is a generalization of a vector with components that are squares of the components of a Gaussian vector, in the sense that the matrix that appears in the Laplace transform of the vector of Gaussian squares is not required to be either symmetric or positive definite. In addition, the power of the determinant in the Laplace transform of the vector of Gaussian squares, which is −1/2, is allowed to be any number less than zero. 相似文献
6.
Serge CohenMakoto Maejima 《Statistics & probability letters》2011,81(11):1664-1669
We study the relationships between the selfdecomposability of marginal distributions or finite dimensional distributions of moving average fractional Lévy processes and distributions of their driving Lévy processes. 相似文献
7.
Ioan Cuculescu 《Journal of multivariate analysis》2003,86(1):48-71
Three types of unimodality (central convex, block, and star) are considered and the corresponding sets of unimodal copulas determined. Examples of star unimodal copulas, absolutely continuous, with a nonnull singular part, and even singular, are given. Necessary and sufficient conditions for a diagonal to be the diagonal section of a star unimodal copula are also indicated. Attention is also paid to the Archimedean case. 相似文献
8.
Weiwei Zhuang 《Insurance: Mathematics and Economics》2009,44(3):409-414
In the literature, orderings of optimal allocations of policy limits and deductibles were established by maximizing the expected utility of wealth of the policyholder. In this paper, by applying the bivariate characterizations of stochastic ordering relations, we reconsider the same model and derive some new refined results on orderings of optimal allocations of policy limits and deductibles with respect to the family of distortion risk measures from the viewpoint of the policyholder. Both loss severities and loss frequencies are considered. Special attention is given to the optimization criteria of the family of distortion risk measures with concave distortions and with only increasing distortions. Most of the results presented in this paper can be applied to some particular distortion risk measures. The results complement and extend the main results in Cheung [Cheung, K.C., 2007. Optimal allocation of policy limits and deductibles. Insurance: Mathematics and Economics 41, 291-382] and Hua and Cheung [Hua, L., Cheung, K.C., 2008a. Stochastic orders of scalar products with applications. Insurance: Mathematics and Economics 42, 865-872]. 相似文献
9.
In this paper we study some stochastic orders of positive dependence that arise when the underlying random vectors are ordered with respect to some multivariate hazard rate stochastic orders, and have the same univariate marginal distributions. We show how the orders can be studied by restricting them to copulae, we give a number of examples, and we study some positive dependence concepts that arise from the new positive dependence orders. We also discuss the relationship of the new orders to other positive dependence orders that have appeared in the literature. 相似文献
10.
Frederic Picard 《Journal of multivariate analysis》2007,98(4):774-788
An inequality of Interpolation type for Multilinear Forms with a two-part dependence condition is proved. It generalizes the work of Bradley and Bryc [Theorem 3.6, Multilinear forms and measures of dependence between random variables, J. Multivariate Anal. 16 (1985) 335-367] and Prakasa Rao [Bounds for rth order joint cumulant under rth order strong mixing, Statist. Probab. Lett. 43 (1999) 427-431]. 相似文献
11.
This paper studies stochastic orderings for folded beta distributions. A necessary and sufficient condition for one folded beta random variable to be larger than another in likelihood ratio order is obtained. The work is motivated by the recent results of Porzio and Ragozini on stochastic orderings for folded binomial distributions. Beta distributions are commonly used to model proportions or probabilities, particularly as conjugate distributions for binomial random variables. Stochastic orderings may arise, for instance, in considerations of fairness in coin flips. 相似文献
12.
Tiantian Mao Taizhong Hu 《Insurance: Mathematics and Economics》2011,48(2):214-216
It is well known that if a random vector with given marginal distributions is comonotonic, it has the largest sum in the sense of the convex order. Cheung (2008) proved that the converse of this assertion is also true, provided that all marginal distribution functions are continuous and that the underlying probability space is atomless. This continuity assumption on the marginals was removed by Cheung (2010). In this short note, we give a new and simple proof of Cheung’s result without the assumption that the underlying probability space is atomless. 相似文献
13.
In this work, we compare conditional distributions derived from bivariate archimedean copulas in terms of their respective variabilities using the dispersive stochastic order. Specifically, we fix the underlying copula and we consider the effect of increasing the second component on the variability of the conditional distribution of the first component. Characterizations are provided in terms of the generator and of the marginal distributions. Several examples involving standard parametric copulas such as Clayton and Frank ones are discussed. 相似文献
14.
John Panaretos 《Annals of the Institute of Statistical Mathematics》1981,33(1):191-198
Summary LetX, Y be two discrete random variables with finite support andX≧Y. Suppose that the conditional distribution ofY givenX can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution
ofX (and hence the joint distribution of (X, Y)) when partial independence only is assumed forY andX−Y. 相似文献
15.
Svante Janson 《Acta Appl Math》1994,34(1-2):5-6
The concentration function of a random variable may be estimated using couplings of the variable with itself.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine. 相似文献
16.
Some equivalent conditions on the classes of lighted-tailed and heavily heavy-tailed and lightly heavy-tailed d. f. s are
introduced. The limit behavior of
and
are discussed. Some properties of the subclass D
K
c
and subclass D
K
c
are obtained.
Supported by the National Natural Science Foundation of China (10271087). 相似文献
17.
Emilio Gómez-Déniz José María SarabiaEnrique Calderín-Ojeda 《Insurance: Mathematics and Economics》2011,48(3):406-412
A new discrete distribution depending on two parameters, α<1,α≠0 and 0<θ<1, is introduced in this paper. The new distribution is unimodal with a zero vertex and overdispersion (mean larger than the variance) and underdispersion (mean lower than the variance) are encountered depending on the values of its parameters. Besides, an equation for the probability density function of the compound version, when the claim severities are discrete is derived. The particular case obtained when α tends to zero is reduced to the geometric distribution. Thus, the geometric distribution can be considered as a limiting case of the new distribution. After reviewing some of its properties, we investigated the problem of parameter estimation. Expected frequencies were calculated for numerous examples, including short and long tailed count data, providing a very satisfactory fit. 相似文献
18.
Frosso S. Makri 《Statistics & probability letters》2011,81(3):402-410
The minimum and maximum distances denoting the extreme numbers of successes between two successive failures in binary sequences, are considered. Exact marginal and joint probability distributions of these statistics are obtained via combinatorial analysis. Applications related to urn models and system reliability are studied and clarify further the theoretical results. 相似文献
19.
We consider the numerical evaluation of one-dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan [H. Abdul-Hamid, J.P. Nolan, Multivariate stable densities as functions of one dimensional projections, J. Multivariate Anal. 67 (1998) 80-89]. In their approach higher order derivatives of one-dimensional densities are used, which seems to be cumbersome in practice. Furthermore there are some difficulties for even dimensions. In order to overcome these difficulties we obtain the explicit finite-interval integral representation of one-dimensional projections for all dimensions. For this purpose we utilize the imaginary part of complex integration, whose real part corresponds to the derivative of the one-dimensional inversion formula. We also give summaries on relations between various parametrizations of stable multivariate density and its one-dimensional projection. 相似文献
20.
Paul B. Larson 《Archive for Mathematical Logic》2005,44(7):817-827
The canonical function game is a game of length ω 1 introduced by W. Hugh Woodin which falls inside a class of games known as Neeman games. Using large cardinals, we show that it is possible to force that the game is not determined. We also discuss the relationship between this result and Σ2 2 absoluteness, cardinality spectra and Π2 maximality for H(ω 2) relative to the Continuum Hypothesis. 相似文献