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Abstract <p>This study investigates asymptotic and bootstrap confidence intervals (CIs) for the ratio of variances of two independent log-normal distributions. Extensive simulations were conducted to evaluate the performance of these CIs under varying sample sizes (10 to 350) and variance ratios, with one variance fixed at 0.1 and the other varying from 0.1 to 2.0. The impacts of balanced and unbalanced designs on sample size were studied. The results reveal that the asymptotic CI performs well for small variance differences, especially with moderate to large sample sizes, while bootstrap CIs outperform it for larger variance differences. Notably, the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8336_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(t\)</EquationSource> <!--LobJMat2560679Ritkumrop-m1--> </InlineEquation>-bootstrap CI excels when both the variance difference and sample sizes are large, whereas the percentile and standard bootstrap CIs are preferable for small variance differences. The study also demonstrates the practical application of these methods using PM2.5 mass concentration data from two industrial sites in Thailand, confirming their effectiveness in real-world scenarios.</p>

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Confidence Estimation of the Ratio of Variances of Two Log-normal Populations

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • Lapasrada Ritkumrop,
  • Puttipong Tantikhajorngosol,
  • Chom Panta

摘要

Abstract

This study investigates asymptotic and bootstrap confidence intervals (CIs) for the ratio of variances of two independent log-normal distributions. Extensive simulations were conducted to evaluate the performance of these CIs under varying sample sizes (10 to 350) and variance ratios, with one variance fixed at 0.1 and the other varying from 0.1 to 2.0. The impacts of balanced and unbalanced designs on sample size were studied. The results reveal that the asymptotic CI performs well for small variance differences, especially with moderate to large sample sizes, while bootstrap CIs outperform it for larger variance differences. Notably, the \(t\) -bootstrap CI excels when both the variance difference and sample sizes are large, whereas the percentile and standard bootstrap CIs are preferable for small variance differences. The study also demonstrates the practical application of these methods using PM2.5 mass concentration data from two industrial sites in Thailand, confirming their effectiveness in real-world scenarios.