Generation of poisson and gamma random vectors with given marginals and covariance matrix

Let be any increasing sequence of integers and M> 1; we connect to them in a very simply way, an increasing unbounded function φ: → R+. Let also X1, X2, · · · be a sequence of i.i.d. random vectors with value in euclidian space Rm. We prove that the cluster set of the sequence almost surely coincides with the unit ball of Rm, if, and only if, the covariance matrix of X1 is the identity matrix of Rm and EX1 is the zero vector of Rm. We define a functional A on the set of increasing sequences of integers as follows:.

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An invariance principle in k-dimensional extended renewal theory

Journal of Applied Probability ◽

10.2307/3213085 ◽

1979 ◽

Vol 16 (3) ◽

pp. 567-574 ◽

Cited By ~ 4

Author(s):

Attila Csenki

Keyword(s):

Limit Theorem ◽

Weak Convergence ◽

Covariance Matrix ◽

Invariance Principle ◽

Exit Time ◽

Renewal Theory ◽

Random Vectors ◽

First Exit Time ◽

First Passage ◽

Passage Times

Let ·be a sequence of k -dimensional i.i.d. random vectors and define the first-passage times for where (cvτ)v, τ= 1,· ··,k is the covariance matrix of In this paper the weak convergence of Zn in (D[0, ∞))k is proved under the assumption (0,∞) for all v = 1, ···, k. We deduce the result from the Donsker invariance principle by means of Theorem 5.5 of Billingsley (1968). This method is also used to derive a limit theorem for the first-exit time Mn = min{Nnt for fixed t1,···, tk > 0. The second result is an extension of a theorem of Hunter (1974) whose method of proof applies only if Ρ (ξ1 [0,∞)k) = 1 and μ ν = tv for all v = 1, ···, k.

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Empirical likelihood ratio under infinite covariance matrix of the random vectors

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2020.1713377 ◽

2020 ◽

pp. 1-8

Author(s):

Conghua Cheng ◽

Zhi Liu

Keyword(s):

Covariance Matrix ◽

Likelihood Ratio ◽

Empirical Likelihood ◽

Random Vectors ◽

Empirical Likelihood Ratio

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High-Dimensional Mahalanobis Distances of Complex Random Vectors

Mathematics ◽

10.3390/math9161877 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1877

Author(s):

Deliang Dai ◽

Yuli Liang

Keyword(s):

Covariance Matrix ◽

Fixed Ratio ◽

Asymptotic Distributions ◽

Random Vectors ◽

Mahalanobis Distances ◽

Random Samples ◽

Sample Covariance ◽

Independent Variable ◽

Non Gaussian ◽

Leave One Out

In this paper, we investigate the asymptotic distributions of two types of Mahalanobis distance (MD): leave-one-out MD and classical MD with both Gaussian- and non-Gaussian-distributed complex random vectors, when the sample size n and the dimension of variables p increase under a fixed ratio c=p/n→∞. We investigate the distributional properties of complex MD when the random samples are independent, but not necessarily identically distributed. Some results regarding the F-matrix F=S2−1S1—the product of a sample covariance matrix S1 (from the independent variable array (be(Zi)1×n) with the inverse of another covariance matrix S2 (from the independent variable array (Zj≠i)p×n)—are used to develop the asymptotic distributions of MDs. We generalize the F-matrix results so that the independence between the two components S1 and S2 of the F-matrix is not required.

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A characterization of matrix variate normal distribution

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171294000475 ◽

1994 ◽

Vol 17 (2) ◽

pp. 341-346 ◽

Cited By ~ 2

Author(s):

Khoan T. Dinh ◽

Truc T. Nguyen

Keyword(s):

Linear Regression ◽

Normal Distribution ◽

Covariance Matrix ◽

The Other ◽

Joint Density ◽

Random Vectors

The joint normality of two random vectors is obtained based on normal conditional with linear regression and constant covariance matrix of each vector given the value of the other without assuming the existence of the joint density. This result is applied to a characterization of matrix variate normal distribution.

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A general approach to correlation and linear dependence between random vectors with regular or singular covariance matrix

Optimization ◽

10.1080/02331937408842211 ◽

1974 ◽

Vol 5 (6) ◽

pp. 487-507

Author(s):

Hans-Peter Höschel

Keyword(s):

Covariance Matrix ◽

Linear Dependence ◽

Random Vectors ◽

Singular Covariance Matrix

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An Alternative Proof for a known Result of Noncentral Wishart Distribution

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800005015 ◽

1997 ◽

Vol 11 (4) ◽

pp. 523-529

Author(s):

Tian-Shyug Lee ◽

Kwang-Chow Chang

Keyword(s):

Covariance Matrix ◽

Multivariate Statistics ◽

Wishart Distribution ◽

Sum Of Squares ◽

Alternative Proof ◽

Random Vectors ◽

Common Variance ◽

Complete Proof ◽

Sample Mean ◽

Detailed Proof

In the theory of multivariate statistics, it is well known that given a sample of n independent p-variate normally distributed random vectors with a common variance-covariance matrix, if at least one of the n vectors has nonzero means, then the sum of squares about the sample mean of the n vectors has a noncentral Wishart distribution. However, a detailed proof for this known result is rarely found in literature. In this paper, we present a formal and complete proof for the well-known result together with an example of its applications.

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