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

Let $\xi_1, \xi_2, \dots$ be i.i.d. non-negative random variables whose tailvaries regularly with index $-1$, let $S_n$ be the sum and $M_n$ the largest ofthe first $n$ values. We clarify for which sequences $x_n\to\infty$ we have$\mathbb P(S_n \ge x_n) \sim \mathbb P(M_n \ge x_n)$ as $n\to\infty$. Outsidethis regime, the typical size of $S_n$ conditioned on exceeding $x_n$ is notcompletely determined by the largest summand and we provide an appropriatecorrection term which involves the integrated tail of $\xi_1$.

Probabilities of large values for sums of i.i.d. non-negative random variables with regular tail of index $-1$