A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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.
Reduced resilience of a globally distributed coccolithophore to ocean acidification: Confirmed up to 2000 generations, supplement to: Jin, Peng; Gao, Kunshan (2016): Reduced resilience of a globally distributed coccolithophore to ocean acidification: Confirmed up to 2000 generations. Marine Pollution Bulletin, 103(1-2), 101-108Jin, Peng; Gao, Kunshan (PANGAEA - Data Publisher for Earth & Environmental Science, 2016) [Dataset]Ocean acidification (OA), induced by rapid anthropogenic CO2 rise and its dissolution in seawater, is known to have consequences for marine organisms. However, knowledge on the evolutionary responses of phytoplankton to OA has been poorly studied. Here we examined the coccolithophore Gephyrocapsa oceanica, while growing it for 2000 generations under ambient and elevated CO2 levels. While OA stimulated growth in the earlier selection period (from generations 700 to 1550), it reduced it in the later selection period up to 2000 generations. Similarly, stimulated production of particulate organic carbon and nitrogen reduced with increasing selection period and decreased under OA up to 2000 generations. The specific adaptation of growth to OA disappeared in generations 1700 to 2000 when compared with that at 1000 generations. Both phenotypic plasticity and fitness decreased within selection time, suggesting that the species' resilience to OA decreased after 2000 generations under high CO2 selection.
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.