A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
Permanent link to this recordhttp://hdl.handle.net/10754/552394
MetadataShow full item record
AbstractSeveral fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.
CitationA non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families 2014, 132:82 Journal of Multivariate Analysis
JournalJournal of Multivariate Analysis
Showing items related by title, author, creator and subject.
Long-tailed distributions in microbial communities in globally distributed sites andStingl, Ulrich (Red Sea Research Center Symposium, King Abdullah University of Science and Technology, 2011-06-28) [Presentation]Taxon-rank abundance curves for naturally occurring microbial populations are Long-tailed distributions.
Distributed terascale volume visualization using distributed shared virtual memoryBeyer, Johanna; Hadwiger, Markus; Schneider, Jens; Jeong, Wonki; Pfister, Hanspeter (2011 IEEE Symposium on Large Data Analysis and Visualization, Institute of Electrical and Electronics Engineers (IEEE), 2011-10) [Conference Paper]Table 1 illustrates the impact of different distribution unit sizes, different screen resolutions, and numbers of GPU nodes. We use two and four GPUs (NVIDIA Quadro 5000 with 2.5 GB memory) and a mouse cortex EM dataset (see Figure 2) of resolution 21,494 x 25,790 x 1,850 = 955GB. The size of the virtual distribution units significantly influences the data distribution between nodes. Small distribution units result in a high depth complexity for compositing. Large distribution units lead to a low utilization of GPUs, because in the worst case only a single distribution unit will be in view, which is rendered by only a single node. The choice of an optimal distribution unit size depends on three major factors: the output screen resolution, the block cache size on each node, and the number of nodes. Currently, we are working on optimizing the compositing step and network communication between nodes. © 2011 IEEE.
Extreme-value limit of the convolution of exponential and multivariate normal distributions: Link to the Hüsler–Reiß distributionKrupskii, Pavel; Joe, Harry; Lee, David; Genton, Marc G. (Journal of Multivariate Analysis, Elsevier BV, 2017-11-02) [Article]The multivariate Hüsler–Reiß copula is obtained as a direct extreme-value limit from the convolution of a multivariate normal random vector and an exponential random variable multiplied by a vector of constants. It is shown how the set of Hüsler–Reiß parameters can be mapped to the parameters of this convolution model. Assuming there are no singular components in the Hüsler–Reiß copula, the convolution model leads to exact and approximate simulation methods. An application of simulation is to check if the Hüsler–Reiß copula with different parsimonious dependence structures provides adequate fit to some data consisting of multivariate extremes.