Scholarlink

Abstract <p>Let <i>n</i> points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior of the sums of functions of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8242_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(m\)</EquationSource> <!--LobJMat2460822Mirakhmedov-m3--> </InlineEquation>-tuples of successive spacings. We derive asymptotic formulas for the expectation and variance of such sums and establish the asymptotic normality of the sums.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Asymptotic Behavior of Sum-functions of \(\boldsymbol{m}\)-Tuples of Uniform Spacings

  • 期刊论文

  • 发表日期：

    2025年3月1日

查看全文
  • Sh. M. Mirakhmedov

摘要

Abstract

Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior of the sums of functions of the \(m\) -tuples of successive spacings. We derive asymptotic formulas for the expectation and variance of such sums and establish the asymptotic normality of the sums.