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 that, for every $0 \leq t \leq 1$, the limiting distribution of thescale-normalized number of key comparisons used by the celebrated algorithmQuickQuant to find the $t$th quantile in a randomly ordered list has aLipschitz continuous density function $f_t$ that is bounded above by $10$.Furthermore, this density $f_t(x)$ is positive for every $x > \min\{t, 1 - t\}$and, uniformly in $t$, enjoys superexponential decay in the right tail. We alsoprove that the survival function $1 - F_t(x) =\int_x^{\infty}\!f_t(y)\,\mathrm{d}y$ and the density function $f_t(x)$ bothhave the right tail asymptotics $\exp [-x \ln x - x \ln \ln x + O(x)]$. We usethe right-tail asymptotics to bound large deviations for the scale-normalizednumber of key comparisons used by QuickQuant.

Density functions for QuickQuant and QuickVal