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<p>The problem of constructing tolerance intervals for the distribution of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X_1-X_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(X_i\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>’s are independent normal random variables, is considered. Approximate methods of finding one-sided, two-sided and equal-tailed tolerance intervals are proposed. The proposed methods are evaluated for their accuracy and compared with already available methods. Using the proposed method, a tolerance interval for the ratio of independent lognormal random variables can be constructed. An example is given to illustrate the methods and some recommendations are made for applications.</p>

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Tolerance Intervals for the Difference Between Two Independent Normal Random Variables

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Ibrahim O. Adenekan,
  • K. Krishnamoorthy

摘要

The problem of constructing tolerance intervals for the distribution of \(X_1-X_2\) X 1 - X 2 , where \(X_i\) X i ’s are independent normal random variables, is considered. Approximate methods of finding one-sided, two-sided and equal-tailed tolerance intervals are proposed. The proposed methods are evaluated for their accuracy and compared with already available methods. Using the proposed method, a tolerance interval for the ratio of independent lognormal random variables can be constructed. An example is given to illustrate the methods and some recommendations are made for applications.