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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper studies the problem of testing the null assumption of no-change in the mean of chronologically ordered independent observations on a random variable $X$ {\it versus} the at most one change in the mean alternative hypothesis. The approach taken is via a Darling-Erd\H{o}s type self-normalized maximal deviation between sample means before and sample means after possible times of a change in the expected values of the observations of a random sample. Asymptotically, the thus formulated maximal deviations are shown to have a standard Gumbel distribution under the null assumption of no change in the mean. A first such result is proved under the condition that $EX^2\log\log (|X|+1)<\infty$, while in the case of a second one, $X$ is assumed to be in a specific class of the domain of attraction of the normal law, possibly with infinite variance.

Change in the mean in the domain of attraction of the normal law via Darling–Erdős theorems