Skip to main content
SpringerLink
Log in

Simultaneous Confidence Intervals for All Differences of Means of Normal Distributions with Unknown Coefficients of Variation

  • Conference paper
  • First Online:
Predictive Econometrics and Big Data (TES 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 753))

Included in the following conference series:

Abstract

This paper presents a procedure for simultaneous confidence interval estimation for the differences of means of several normal populations with unknown coefficients of variation. The proposed approaches are a generalized confidence interval approach (GCI approach) and method of variance estimates recovery approach (MOVER approach). A Monte Carlo simulation was used to evaluate the performance in terms of coverage probability, average width and standard error. The simulation results indicated that the GCI and MOVER approaches are satisfactory in terms of the coverage probability, but the average widths of the MOVER approach are slightly shorter than the average widths of the GCI approach. The proposed approaches are illustrated by an example.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bhat, K.K., Rao, K.A.: On tests for a normal mean with known coefficient of variation. Inter. Stat. Rev. 75, 170–182 (2007)

    Article  Google Scholar 

  2. Donner, A., Zou, G.Y.: Closed-form confidence intervals for function of the normal standard deviation. Stat. Meth. Med. Res. 21, 347–359 (2010)

    Article  MathSciNet  Google Scholar 

  3. Gleser, L.J., Healy, J.D.: Estimating the mean of a normal distribution with known coefficient of variation. J. Am. Stat. Assoc. 71, 977–981 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  4. Khan, R.A.: A note on estimating the mean of a normal distribution with known coefficient of variation. J. Am. Stat. Assoc. 63, 1039–1041 (1968)

    MATH  Google Scholar 

  5. Kharrati-Kopaei, M., Malekzadeh, A., Sadooghi-Alvandi, M.: Simultaneous fiducial generalized confidence intervals for the successive differences of exponential location parameters under heteroscedasticity. Stat. Prob. Lett. 83, 1547–1552 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kharrati-Kopaei, M.: A note on the simultaneous confidence intervals for the successive differences of exponential location parameters under heteroscedasticity. Stat. Meth. 22, 1–7 (2015)

    Article  MathSciNet  Google Scholar 

  7. Krishnamoorthy, K., Lu, Y.: Inference on the common means of several normal populations based on the generalized variable method. Biometrics 59, 237–247 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, J., Song, W., Shi, J.: Parametric bootstrap simultaneous confidence intervals for differences of means from several two-parameter exponential distributions. Stat. Prob. Lett. 106, 39–45 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Malley, J.D.: Simultaneous confidence intervals for ratios of normal means. J. Am. Stat. Assoc. 77, 170–176 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  10. Niwitpong, S.: Confidence intervals for the normal mean with known coefficient of variation. World Acad. Sci. Eng. Technol. 6, 1365–1368 (2012)

    MathSciNet  Google Scholar 

  11. Niwitpong, S.: Confidence intervals for the normal mean with a known coefficient of variation. Far East J. Math. Sci. 97, 711–727 (2015)

    MATH  Google Scholar 

  12. Niwitpong, S., Koonprasert, S., Niwitpong, S.: Confidence interval for the difference between normal population means with known coefficients of variation. Appl. Math. Sci. 6, 47–54 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Niwitpong, S., Niwitpong, S.: On simple confidence intervals for the normal mean with a known coefficient of variation. World Acad. Sci. Eng. Technol. 7, 1444–1447 (2013)

    MATH  Google Scholar 

  14. Niwitpong, S., Niwitpong, S.: Confidence intervals for the difference between normal means with known coefficients of variation. Ann. Oper. Res. 247, 1–15 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sadooghi-Alvandi, S.M., Malekzadeh, A.: Simultaneous confidence intervals for ratios of means of several lognormal distributions: a parametric bootstrap approach. Comput. Stat. Data Anal. 69, 133–140 (2014)

    Article  MathSciNet  Google Scholar 

  16. Sahai, A.: On an estimator of normal population mean and UMVU estimation of its relative efficiency. Appl. Math. Comput. 152, 701–708 (2004)

    MathSciNet  MATH  Google Scholar 

  17. Sahai, A., Acharya, R.M.: Iterative estimation of normal population mean using computational-statistical intelligence. Comput. Sci. Technol. 4, 500–508 (2016)

    Google Scholar 

  18. Sangnawakij, P., Niwitpong, S., Niwitpong, S.: Confidence intervals for the ratio of coefficients of variation of the gamma distributions. Lecture Notes in Computer Science, vol. 9376, pp. 193–203 (2015)

    Google Scholar 

  19. Sangnawakij, P., Niwitpong, S.: Confidence intervals for coefficients of variation in two-parameter exponential distribution. Commun. Stat. Simul. Comput. 46, 6618–6630 (2017)

    Article  Google Scholar 

  20. Searls, D.T.: The utilization of a known coefficient of variation in the estimation procedure. J. Am. Stat. Assoc. 59, 1225–1226 (1964)

    Article  MATH  Google Scholar 

  21. Srivastava, V.K.: On the use of coefficient of variation in estimating mean. J. Indian Soc. Agric. Stat. 26, 33–36 (1974)

    Google Scholar 

  22. Srivastava, V.K.: A note on the estimation of mean in normal population. Metrika 27, 99–102 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  23. Srivastava, V.K., Singh, R.S.: Uniformly minimum variance unbiased estimator of efficiency ratio in estimation of normal population mean. Stat. Prob. Lett. 10, 241–245 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sodanin, S., Niwitpong, S., Niwitpong, S.: Confidence intervals for common mean of normal distributions with known coefficient of variation. Lecture Notes in Computer Science, vol. 9978, pp. 574–585 (2016)

    Google Scholar 

  25. Thangjai, W., Niwitpong, S., Niwitpong, S.: Confidence intervals for the common mean of several normal populations with unknown coefficients of variation. Commun. Stat. Simul. Comput. (2017, Submitted)

    Google Scholar 

  26. Tian, L.: Inferences on the common coefficient of variation. Stat. Med. 24, 2213–2220 (2005)

    Article  MathSciNet  Google Scholar 

  27. Tian, L., Wu, J.: Inferences on the common mean of several log-normal populations: the generalized variable approach. Biometrical J. 49, 944–951 (2007)

    Article  MathSciNet  Google Scholar 

  28. Walpole, R.E., Myers, R.H., Myers, S.L., Ye, K.: Probability and Statistics for Engineers and Scientists. Prentice Hall, Upper Saddle River (2012)

    MATH  Google Scholar 

  29. Weerahandi, S.: Generalized confidence intervals. J. Am. Stat. Assoc. 88, 899–905 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  30. Ye, R.D., Ma, T.F., Wang, S.G.: Inferences on the common mean of several inverse Gaussian populations. Comput. Stat. Data Anal. 54, 906–915 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhang, G.: Simultaneous confidence intervals for several inverse Gaussian populations. Stat. Prob. Lett. 92, 125–131 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  32. Zou, G.Y., Donner, A.: Construction of confidence limits about effect measures: a general approach. Stat. Med. 27, 1693–1702 (2008)

    Article  MathSciNet  Google Scholar 

  33. Zou, G.Y., Taleban, J., Hao, C.Y.: Confidence interval estimation for lognormal data with application to health economics. Comput. Stat. Data Anal. 53, 3755–3764 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The first author gratefully acknowledges the financial support from Science Achievement Scholarship of Thailand.

Author information

Authors and Affiliations

  1. Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Warisa Thangjai, Sa-Aat Niwitpong & Suparat Niwitpong

Authors
  1. Warisa Thangjai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sa-Aat Niwitpong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Suparat Niwitpong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Warisa Thangjai .

Editor information

Editors and Affiliations

  1. Computer Science Department, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  2. International College, Chiang Mai University, Chiang Mai, Thailand

    Songsak Sriboonchitta

  3. International College, Chiang Mai University, Chiang Mai, Thailand

    Nopasit Chakpitak

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Thangjai, W., Niwitpong, SA., Niwitpong, S. (2018). Simultaneous Confidence Intervals for All Differences of Means of Normal Distributions with Unknown Coefficients of Variation. In: Kreinovich, V., Sriboonchitta, S., Chakpitak, N. (eds) Predictive Econometrics and Big Data. TES 2018. Studies in Computational Intelligence, vol 753. Springer, Cham. https://doi.org/10.1007/978-3-319-70942-0_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70942-0_48

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70941-3

  • Online ISBN: 978-3-319-70942-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation