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

The leading term in the normal approximation to the distribution of Student'st statistic is derived in a general setting, with the sole assumption beingthat the sampled distribution is in the domain of attraction of a normal law.The form of the leading term is shown to have its origin in the way in whichextreme data influence properties of the Studentized sum. The leading-termapproximation is used to give the exact rate of convergence in the centrallimit theorem up to order n^{-1/2}, where n denotes sample size. It is provedthat the exact rate uniformly on the whole real line is identical to the exactrate on sets of just three points. Moreover, the exact rate is identical tothat for the non-Studentized sum when the latter is normalized for scale usinga truncated form of variance, but when the corresponding truncated centeringconstant is omitted. Examples of characterizations of convergence rates arealso given. It is shown that, in some instances, their validity uniformly onthe whole real line is equivalent to their validity on just two symmetricpoints.

Exact convergence rate and leading term in central limit theorem for student’s t statistic