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Abstract <p>In this paper, using known values of the expectations of upper record values <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{E}(R_{2}),\ldots,\textrm{E}(R_{m})\)</EquationSource> <!--MMStat2670001Balakrishnan-m1--> </InlineEquation>, for some <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(m\in\left\{2,\ldots,n-1\right\}\)</EquationSource> <!--MMStat2670001Balakrishnan-m2--> </InlineEquation>, we derive improved bounds for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{E}(R_{n})\)</EquationSource> <!--MMStat2670001Balakrishnan-m3--> </InlineEquation>. Further improvements are obtained in the case of a symmetric underlying distribution. Numerical illustrations of the results are provided for the standard normal distribution. Finally, extensions of the results to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(k\)</EquationSource> <!--MMStat2670001Balakrishnan-m4--> </InlineEquation>-record values are detailed.</p>

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Improved Imputation-Type Bounds for Means of Record Values for General and Symmetric Distributions

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • N. Balakrishnan,
  • Anja B. Schmiedt

摘要

Abstract

In this paper, using known values of the expectations of upper record values \(\textrm{E}(R_{2}),\ldots,\textrm{E}(R_{m})\) , for some \(m\in\left\{2,\ldots,n-1\right\}\) , we derive improved bounds for \(\textrm{E}(R_{n})\) . Further improvements are obtained in the case of a symmetric underlying distribution. Numerical illustrations of the results are provided for the standard normal distribution. Finally, extensions of the results to \(k\) -record values are detailed.