English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Gaussian correlation inequality (GCI) for symmetrical n-rectangles isimproved if the absolute components have a joint cumulative distribution (cdf)which is MTP2 (multivariate totally positive of order 2). Inequalities of thehere given type hold at least for all MTP2-cdfs on R^n or (0,infinity)^n witheverywhere positive smooth densities. In particular, at least some infinitelydivisible multivariate chi-square distribution functions (gamma distributionsin the sense of Krishnamoorthy and Parthasarathy) with any positive real"degree of freedom" are shown to be MTP2. Moreover, further numericallycalculable probability inequalities for a broad class of multivariate gammadistributions are derived and a different improvement for inequalities of theGCI-type - and of a similar type with three instead of two groups of components- with more special correlation structures. The main idea behind theseinequalities is to find for a given correlation matrix with positivecorrelations a further correlation matrix with smaller correlations whoseinverse is an M-matrix and where the corresponding multivariate gammadistribution function is numerically available.

Some improved Gaussian correlation inequalities for symmetrical  n-rectangles extended to some multivariate gamma distributions and some  further probability inequalities