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

In this work we present concentration inequalities for the sum $S_n$ ofindependent integer-valued not necessary indentically distributed randomvariables, where each variable has tail function that can be bounded by somepower function with exponent $-\alpha$. We show that when $0<\alpha\leq 1$,then the sum does not have finite expectation, however, with high probabilitywe have that $|S_n|=O\left(n^{1/\alpha}\right)$. When $\alpha>1$, then the sum$S_n$ is concentrated around its mean.  Since the r.vs. that constitute the sum has tails, which can be bounded bysome power function, it follows that results of this paper are applicable to awide range of different distributions, including the exponentially decayingones.

Concentration inequalities for sums of random variables, each having power bounded tails