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 X 1 , X2 , ..., X,. be independent and identically distributed random variables subject to a continuous distribution function F, let X 1 ,,X2 ,., ...,X,, be the corresponding order statistics, and write P(Xt+, Xk, ? x) P(X,_k ^! x) (x ^! 0) (0) where n.k and s are fixed integers with Ic + s n. It is an old question if condition (0) implies that F is of exponential type. In [8] we showed among others that condition (0) can be greatly relaxed; namely, it can be replaced by asymptotic relations (either as x oe or x j 0) to derive this very result. Using a theorem on integrated Cauchy functional equations and in essential way a result of [8] we find now a more elegant and deeper theorem on this subject. The case of lattice distributions is also considered and some new problems are stated.

Characterization of the Exponential Distribution by Properties of the Difference $X_{k+s:n} – X_{k:n}$ of Order Statistics