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

We prove abstract bounds on the Wasserstein and Kolmogorov distances betweennon-randomly centered random sums of real i.i.d. random variables with a finitethird moment and the standard normal distribution. Except for the case of meanzero summands, these bounds involve a coupling of the summation index with itssize biased distribution as was previously considered in \cite{GolRin96} forthe normal approximation of nonnegative random variables. When beingspecialized to concrete distributions of the summation index like the Binomial,Poisson and Hypergeometric distribution, our bounds turn out to be of thecorrect order of magnitude.

New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods