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International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making

IUKM 2015: Integrated Uncertainty in Knowledge Modelling and Decision Making pp 183–192Cite as

Approximate Confidence Interval for the Ratio of Normal Means with a Known Coefficient of Variation

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9376))

Abstract

An approximate confidence interval for the ratio of normal population means with a known coefficient of variation is proposed. This has applications in the area of bioassay and bioequivalence when the scientist knows the coefficient of variation of the control group. The proposed confidence interval is based on the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval. Simulation results show that the proposed confidence interval performs as well as the existing one in terms of coverage probability and expected length. However, the approximate confidence interval is very easy to calculate compared with the exact confidence interval.

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References

  1. Bliss, C.I.: The Calculation of the Dose-Mortality Curve. Ann. Appl. Biol. 22, 134–167 (1935)

    Article  Google Scholar 

  2. Bliss, C.I.: The Comparison of Dose-Mortality Data. Ann. Appl. Biol. 22, 309–333 (1935)

    Google Scholar 

  3. Irwin, J.O.: Statistical Method Applied to Biological Assay. J. R. Stat. Soc. Ser B. 4, 1–60 (1937)

    MATH  Google Scholar 

  4. Fieller, E.C.: A Fundamental Formula in the Statistics of Biological Assay and Some Applications. Q. J. Pharm. Pharmacol. 17, 117–123 (1944)

    Google Scholar 

  5. Fieller, E.C.: Some Problems in Interval Estimation. J. R. Stat. Soc. Ser B. 16, 175–185 (1954)

    MathSciNet  MATH  Google Scholar 

  6. Finney, D.J.: The Principles of the Biological Assay (with discussion). J. R. Stat. Soc. Ser B. 1, 46–91 (1947)

    Google Scholar 

  7. Finney, D.J.: The Meaning of Bioassay. Biometrics 21, 785–798 (1965)

    Article  Google Scholar 

  8. Cox, C.P.: Interval Estimates for the Ratio of the Means of Two Normal Populations with Variances Related to the Means. Biometrics 41, 261–265 (1985)

    Article  MATH  Google Scholar 

  9. Srivastava, M.S.: Multivariate Bioassay, Combination of Bioassays and Fieller’s Theorem. Biometrics 42, 131–141 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kelly, G.E.: The Median Lethal Dose-Design and Estimation. The Statistician 50, 41–50 (2000)

    MathSciNet  Google Scholar 

  11. Lee, J.C., Lin, S.H.: Generalized Confidence Intervals for the Ratio of Means of Two Normal Populations. J. Stat. Plan. Infer. 123, 49–60 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Vuorinen, J., Tuominen, J.: Fieller’s Confidence Intervals for the Ratio of Two Means in the Assessment of Average Bioequivalence from Crossover Data. Stat. Med. 13, 2531–2545 (1994)

    Article  Google Scholar 

  13. Koschat, M.A.: A Characterization of the Fieller Solution. Ann. Statist. 15, 462–468 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  14. Niwitpong, S., Koonprasert, S., Niwitpong, S.: Confidence Intervals for the Ratio of Normal Means with a Known Coefficient of Variation. Adv. Appl. Stat. 25, 47–61 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Weerahandi, S.: Generalized Confidence Intervals. J. Amer. Statist. Assoc. 88, 899–905 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ihaka, R., Gentleman, R.: R: A Language for Data Analysis and Graphics. J. Comp. Graph. Stat. 5, 299–314 (1996)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathumthani, 12121, Thailand

    Wararit Panichkitkosolkul

Authors
  1. Wararit Panichkitkosolkul
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Correspondence to Wararit Panichkitkosolkul .

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Editors and Affiliations

  1. Science and Technology, Japan Advanced Institute of, Nomi, Japan

    Van-Nam Huynh

  2. Science, Dept of Systems Innovation, Osaka University,Graduate School of, Osaka, Japan

    Masahiro Inuiguchi

  3. Université de Technologie de Compiègne, Compiègne, France

    Thierry Demoeux

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Panichkitkosolkul, W. (2015). Approximate Confidence Interval for the Ratio of Normal Means with a Known Coefficient of Variation. In: Huynh, VN., Inuiguchi, M., Demoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2015. Lecture Notes in Computer Science(), vol 9376. Springer, Cham. https://doi.org/10.1007/978-3-319-25135-6_18

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  • DOI: https://doi.org/10.1007/978-3-319-25135-6_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25134-9

  • Online ISBN: 978-3-319-25135-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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