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

Variance-Gamma distributions are widely used in financial modelling andcontain as special cases the normal, Gamma and Laplace distributions. In thispaper we extend Stein's method to this class of distributions. In particular,we obtain a Stein equation and smoothness estimates for its solution. ThisStein equation has the attractive property of reducing to the known normal andGamma Stein equations for certain parameter values. We apply these results andlocal couplings to bound the distance between sums of the form$\sum_{i,j,k=1}^{m,n,r}X_{ik}Y_{jk}$, where the $X_{ik}$ and $Y_{jk}$ areindependent and identically distributed random variables with zero mean, bytheir limiting Variance-Gamma distribution. Through the use of novel symmetryarguments, we obtain a bound on the distance that is of order $m^{-1}+n^{-1}$for smooth test functions. We end with a simple application to binary sequencecomparison.

Variance-Gamma approximation via Stein's method