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/

Zendy Plus

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

Zendy Tools

Zendy Open

In Nevzorov's $F^\alpha$-scheme, one deals with a sequence of independentrandom variables whose distribution functions are all powers of a commoncontinuous distribution function. A key property of the $F^\alpha$-scheme isthat the record indicators for such a sequence are independent. This allows oneto obtain several important limit theorems for the total number of records inthe sequence up to time $n\to\infty$. We extend these theorems to a much moregeneral class of sequences of random variables obeying a "threshold$F^\alpha$-scheme" in which the distribution functions of the variables areclose to the powers of a common $F$ only in their right tails, above certainnon-random non-decreasing threshold levels. Of independent interest is thecharacterization of the growth rate for extremal processes that we derived inorder to be able to verify the conditions of our main theorem. We alsoestablish the asymptotic pair-wise independence of record indicators in aspecial case of threshold $F^\alpha$-schemes.

Limit theorems for record indicators in threshold $F^\alpha$-schemes