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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $X^1, ..., X^k$ and $Y^1, ..., Y^m$ be jointly independent copies ofrandom variables $X$ and $Y$, respectively. For a fixed total number $n$ ofrandom variables, we aim at maximising $M(k,m):= E \max \{X^1, ..., X^k, Y^1,>..., Y^{m} \}$ in $k = n-m\ge 0$, which corresponds to maximising the expectedlifetime of an $n$-component parallel system whose components can be chosenfrom two different types. We show that the lattice $\{M(k,m): k, m\ge 0\}$ isconcave, give sufficient conditions on $X$ and $Y$ for M(n,0) to be always orultimately maximal and derive a bound on the number of sign changes in thesequence $M(n,0)-M(0,n)$, $n\ge 1$. The results are applied to a mixedpopulation of Bienayme-Galton-Watson processes, with the objective to derivethe optimal initial composition to maximise the expected time to extinction.

On the Expectations of Maxima of Sets of Independent Random Variables