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Methods for Testing the Difference Between Two Signal-to-Noise Ratios of Log-Normal Distributions

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12482))

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Abstract

This study presents three methods for testing the difference between two signal-to-noise ratios (SNRs) of log-normal distributions. The proposed statistical tests were based on the generalized confidence interval (GCI) approach, the large sample (LS) approach and the method of variance estimates recovery (MOVER) approach. To compare the performance of the proposed statistical tests, a simulation study was conducted under several values of SNRs in log-normal distributions. The performance of the statistical tests was compared based on the empirical size and power of the test. The simulation results showed that the statistical test based on the GCI approach performed better than the statistical tests based on the LS and the MOVER approaches in terms of the attained nominal significance level and empirical power of the test and is thus recommended for researchers. The performance of the proposed statistical tests is also illustrated through a numerical example.

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References

  1. Panichkitkosolkul, W.: Improved confidence intervals for a coefficient of variation of a normal distribution. Thai. Stat. 7(2), 193–199 (2009)

    MathSciNet  MATH  Google Scholar 

  2. Acharya, T., Ray, A.K.: Image Processing: Principles and Applications. Wiley, Hoboken (2005)

    Book  Google Scholar 

  3. Russ, C.J.: The Image Processing Handbook. CRC Press, Boca Raton (2011)

    MATH  Google Scholar 

  4. Rafael, C.G., Richard, E.W.: Digital Image Processing. Prentice Hall, Upper Saddle River (2008)

    Google Scholar 

  5. Tania, S.: Image Fusion: Algorithms and Applications. Academic Press, San Diego (2008)

    Google Scholar 

  6. Kapur, K., Chen, G.: Signal-to-noise ratio development for quality engineering. Qual. Reliab. Eng. Int. 4(2), 133–141 (1988)

    Article  Google Scholar 

  7. Kaufman, L., Kramer, D.M., Crooks, L.E., Ortendahl, D.A.: Measuring signal-to-noise ratios in MR imaging. Radiology 173(1), 265–267 (1989)

    Article  Google Scholar 

  8. McGibney, G., Smith, M.R.: An Unbiased signal-to-noise ratio measure for magnetic resonance images. Med. Phys. 20(4), 1077–1079 (1993)

    Article  Google Scholar 

  9. Firbank, M.J., Coulthard, A., Harrison, R.M., Williams, E.D.: A comparison of two methods for measuring the signal to noise ratio on MR images. Phys. Med. Biol. 44(12), 261–264 (1999)

    Article  Google Scholar 

  10. Czanner, G., et al.: Measuring the signal-to-noise ratio of a neuron. Nat. Acad. Sci. 112(23), 7141–7146 (2015)

    Article  Google Scholar 

  11. Patil, A.N., Hublikar, S.P., Faria, L.S., Khadilkar, S.S.: Improving service quality of hotel business using collective QFD and signal to noise ratio. OmniScience: Multi-Disc. J. 9(1), 34–41 (2019)

    Google Scholar 

  12. Liu, S.T.: A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio. Ann. Oper. Res. 261(1), 207–232 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  13. Thangjai, W., Niwitpong, S.-A.: Confidence intervals for the signal-to-noise ratio and difference of signal-to-noise ratios of log-normal distributions. Stats 2, 164–173 (2019)

    Article  Google Scholar 

  14. Panichkitkosolkul, W., Tulyanitikul, B.: Performance of statistical methods for testing the signal-to-noise ratio of a log-normal distribution. In: 2020 IEEE 7th International Conference on Industrial Engineering and Applications (ICIEA), Bangkok, Thailand, pp. 656–661 (2020)

    Google Scholar 

  15. Thangjai, W., Niwitpong, S.-A., Niwitpong, S.: Simultaneous fiducial generalized confidence intervals for all differences of coefficients of variation of log-normal distributions. In: Huynh, V.-N., Inuiguchi, M., Le, B., Le, B.N., Denoeux, T. (eds.) IUKM 2016. LNCS (LNAI), vol. 9978, pp. 552–561. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49046-5_47

    Chapter  MATH  Google Scholar 

  16. Loève, M.: Probability Theory I: Graduate Texts in Mathematics. Springer, New York (1977). https://doi.org/10.1007/978-1-4684-9464-8

    Book  Google Scholar 

  17. Weerahandi, S.: Generalized confidence intervals. J. Am. Stat. Assoc. 88(423), 899–906 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  18. Jose, S., Thomas, S.: Interval estimation of the overlapping coefficient of two normal distributions: one way ANOVA with random effects. Thai. Stat. 17(1), 84–92 (2019)

    MATH  Google Scholar 

  19. Thangjai, W., Niwitpong, S.-A., Niwitpong, S.: Simultaneous confidence intervals for all differences of means of normal distributions with unknown coefficients of variation. In: Kreinovich, V., Sriboonchitta, S., Chakpitak, N. (eds.) TES 2018. SCI, vol. 753, pp. 670–682. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-70942-0_48

    Chapter  MATH  Google Scholar 

  20. Tian, L., Cappelleri, J.C.: A new approach for interval estimation and hypothesis testing of a certain intraclass correlation coefficient: the generalized variable method. Stat. Med. 23(13), 2125–2135 (2004)

    Article  Google Scholar 

  21. Donner, A., Zou, G.Y.: Closed-form confidence intervals for functions of the normal mean and standard deviation. Stat. Methods Med. Res. 21(4), 347–359 (2012)

    Article  MathSciNet  Google Scholar 

  22. Zou, G.Y., Taleban, J., Huo, C.Y.: Confidence interval estimation for lognormal data with application to health economics. Comput. Stat. Data Anal. 53(11), 3755–3764 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Li, H.Q., Tang, M.L., Poon, W.Y., Tang, N.S.: Confidence intervals for difference between two Poisson rates. Commun. Stat.-Simul. Comput. 40(9), 1478–1493 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Newcombe, R.G.: MOVER-R confidence intervals for ratios and products of two independently estimated quantities. Stat. Methods Med. Res. 25(5), 1774–1778 (2016)

    Article  MathSciNet  Google Scholar 

  25. Sangnawakij, P., Niwitpong, S.-A.: Confidence intervals for coefficients of variation in two-parameter exponential distributions. Commun. Stat.-Simul. Comput. 46(8), 6618–6630 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zou, G.Y., Huang, W., Zhang, X.: A note on confidence interval estimation for a linear function of binomial proportions. Comput. Stat. Data Anal. 53(4), 1080–1085 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ihaka, R., Gentleman, R.: R: a language for data analysis and graphics. J. Comput. Graph. Stat. 5(3), 299–314 (1996)

    Google Scholar 

  28. Bhat, K., Rao, K.A.: On tests for a normal mean with known coefficient of variation. Int. Stat. Rev. 75(2), 170–182 (2007)

    Article  Google Scholar 

  29. Panichkitkosolkul, W.: A unit root test based on the modified least squares estimator. Sains Malaysiana 43(10), 1623–1633 (2014)

    MATH  Google Scholar 

  30. Niwitpong, S., Kirdwichai, P.: Adjusted Bonett Confidence interval for standard deviation of non-normal distribution. Thai. Stat. 6(1), 1–6 (2008)

    MathSciNet  MATH  Google Scholar 

  31. McDonald, C.J., Blevins, L., Tierney, W.M., Martin, D.K.: The Regenstrief medical records. MD Comput. 5(5), 34–47 (1988)

    Google Scholar 

  32. Zhou, X.H., Gao, S., Hui, S.L.: Methods for comparing the means of two independent log-normal samples. Biometrics 53(3), 1129–1135 (1997)

    Article  MATH  Google Scholar 

  33. Jafari, A.A., Abdollahnezhad, K.: Inferences on the means of two log-normal distributions: a computational approach test. Commun. Stat.-Simul. Comput. 44(7), 1659–1672 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

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

    Wararit Panichkitkosolkul & Kamon Budsaba

Authors
  1. Wararit Panichkitkosolkul
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  2. Kamon Budsaba
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Correspondence to Wararit Panichkitkosolkul .

Editor information

Editors and Affiliations

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

    Van-Nam Huynh

  2. University of Hyogo, Kobe, Japan

    Tomoe Entani

  3. Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani, Thailand

    Chawalit Jeenanunta

  4. Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

  5. Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani, Thailand

    Pisal Yenradee

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Panichkitkosolkul, W., Budsaba, K. (2020). Methods for Testing the Difference Between Two Signal-to-Noise Ratios of Log-Normal Distributions. In: Huynh, VN., Entani, T., Jeenanunta, C., Inuiguchi, M., Yenradee, P. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2020. Lecture Notes in Computer Science(), vol 12482. Springer, Cham. https://doi.org/10.1007/978-3-030-62509-2_32

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  • DOI: https://doi.org/10.1007/978-3-030-62509-2_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62508-5

  • Online ISBN: 978-3-030-62509-2

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