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Confidence Intervals for Coefficient of Variation of Inverse Gaussian Distribution

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Published:25 May 2020Publication History

ABSTRACT

The coefficient of variation is an useful indicator to measure and compare separated data in different units. This paper proposes the new confidence interval for the single coefficient of variation and the difference between coefficients of variation of Inverse Gaussian distribution using the generalized confidence interval (GCI) and the bootstrap percentile confidence interval. A Monte Carlo simulation is used to construct and compare the performance of these confidence intervals based on the coverage probability and average length. The results of the simulation study showed that the GCI is an appropriate method to construct the confidence interval for the single coefficient of variation and the difference between coefficients of variation. The proposed approaches are illustrated based on the real data.

References

  1. AG Shaper, SJ Pocock, AN Phillips and M Walker (1986). Identifying men at high risk of heart attacks: strategy for use in general practice. BMJ, 293, 474--478.Google ScholarGoogle ScholarCross RefCross Ref
  2. A Wongkhao, S Niwitpong and S Niwitpong (2015). Confidence intervals for the ratio of two independent coefficients of variation of normal distribution. Far East Journal of Mathematical Sciences, 98(6), 741--757.Google ScholarGoogle ScholarCross RefCross Ref
  3. B Efron and RJ Tibshirani (1993). An Introduction to Bootstrap, Chapman & Hall/CRC, Monographs on Statistics and Applied Probability, USA.Google ScholarGoogle ScholarCross RefCross Ref
  4. DK Srivastava and GS Mudholkar (2003). Goodness-of-fit tests for univariate and multivariate normal models. In: Khattree, R., Rao, C.R. (Eds.), Handbook of Statistics, Elsevier Science, Amsterdam, 22, 869--906.Google ScholarGoogle Scholar
  5. E Schrödinger (1915). Zür theorie der fall-und steigversuche an teilchen mit Brownscer bewegung. Physikaliche Zeitschrift, 16, 289--295.Google ScholarGoogle Scholar
  6. HE Akyuz and H Gamgam (2017). Bootstrap and jackknife approximate confidence intervals and performance comparisons for population coefficient of variation. Communication in Statistics: Simulation and Computation.Google ScholarGoogle Scholar
  7. HK Hsieh (1990). Inferences on the coefficient of variation of an inverse Gaussian distribution. Communications in Statistics, 19(5), 1589--1605.Google ScholarGoogle ScholarCross RefCross Ref
  8. K Krishnamoorthy and L Tian (2008). Inferences on the difference and ratio of the means of two inverse Gaussian distributions. J. Statist. Plann, Inference, 133(7), 2082--2089.Google ScholarGoogle ScholarCross RefCross Ref
  9. K Krishnamoorthy and Y Lu (2003). Inference on the common mean of several normal populations based on the generalized variable method. Biometrics, 59(2), 237--247.Google ScholarGoogle ScholarCross RefCross Ref
  10. L Tian (2005). Inferences on the common coefficient of variation. Statistics in Medicine, 24(14), 2213--2220.Google ScholarGoogle ScholarCross RefCross Ref
  11. L Tian and J Wu (2007). Inferences on the mean response in a log-regression model: The generalized variable approach. Stat. Med. 26, 5180--5188.Google ScholarGoogle ScholarCross RefCross Ref
  12. M Gulhar, BM Golam Kibria, AN Albatineh, and NU Ahmed (2012). A comparison of some confidence intervals for estimating the population coefficient of variation: A simulation study. Statistics and Operations Research Transactions, 36(1), 45--68.Google ScholarGoogle Scholar
  13. N Buntao and S Niwitpong (2013). Confidence intervals for the ratio of coefficients of variation of delta-Lognormal Distribution. Applied Mathematical Science, 7(77), 3811--3818.Google ScholarGoogle ScholarCross RefCross Ref
  14. P DE, JB Ghosh and CE Wells (1996) Scheduling to minimize the coefficient of variation. Int. J. Production Economics, 44(3), 249--253.Google ScholarGoogle ScholarCross RefCross Ref
  15. P Sangnawakij and S Niwitpong (2017). Confidence intervals for coefficients of variation in two-parameter exponential distributions. Communications in Statistics- Simulation and Computation, 46(8), 6618--6630.Google ScholarGoogle ScholarCross RefCross Ref
  16. R Mahmoudvand And H Hassani. (2009). Two new confidence intervals for the coefficient of variation in a normal distribution. Journal of Applied Statistics, 36(4), 429--442.Google ScholarGoogle ScholarCross RefCross Ref
  17. RD Ye and SG Wang (2008). Generalized inferences on the common mean in MANOVA models. Comm. Statist. Theory Methods, 37(14), 2291--2303.Google ScholarGoogle ScholarCross RefCross Ref
  18. RD YE, TF Ma and SG Wang (2010). Inferences on the common mean of several inverse Gaussian populations. Comput Stat Data Anal, 54, 906--915.Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. RJ Pavur, RL Edgeman and RC Scott (1992). Quadratic statistics for the goodness-of --fit test of the inverse Gaussian distribution. IEEE Transactions on Reliability, 41(1), 118--123.Google ScholarGoogle ScholarCross RefCross Ref
  20. RS Chhikara and JL Folks (1977). The inverse Gaussian distribution as a lifetime model.Technometrics, 19, 461--468.Google ScholarGoogle Scholar
  21. RS Chhikara and JL Folks (1989). The inverse Gaussian distribution. Marcel Dekker, New York.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. S Banik and BMG Kibria (2011). Estimating the population coefficient of variation by confidence intervals. Communication in Statistics- Simulation and Computation, 40(8), 1236--1261.Google ScholarGoogle ScholarCross RefCross Ref
  23. S Weerahandi (1993). Generalized confidence intervals. J. Amer. Statist. Assoc, 88(423), 899--905.Google ScholarGoogle ScholarCross RefCross Ref
  24. SH Lin and JC Lee (2005). Generalized inferences on the common mean of several normal populations. J. Statist. Plann. Inference, 134(2), 568--582.Google ScholarGoogle ScholarCross RefCross Ref
  25. H Lin, JC Lee and RS Wang (2007). Generalized inferences on the common mean vector of several multivariate normal populations. J. Statist. Plann. Inference, 137(7), 2240--2249.Google ScholarGoogle ScholarCross RefCross Ref
  26. TM Young, DG Perhac, FM Guess, and RV León (2008). Bootstrap confidence intervals for percentiles of reliability data for wood-plastic composits. Forest Products Journal, 58(11), 106--114.Google ScholarGoogle Scholar
  27. X Liu, N Li and Y Hu (2015). Combining inferences on the common mean of several inverse Gaussian distributions based on confidence distribution. Stat Probab Lett. 105, 136--142.Google ScholarGoogle ScholarCross RefCross Ref
  28. YL Tsim, SP Yip, KS Tsang, KF Li and HF Wong (1991). Haematology and Serology. In Annual Report, Hong Kong Medical Technology Association Quality Assurance Programme, 25--40.Google ScholarGoogle Scholar

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    • Published in

      cover image ACM Other conferences
      ICVISP 2019: Proceedings of the 3rd International Conference on Vision, Image and Signal Processing
      August 2019
      584 pages
      ISBN:9781450376259
      DOI:10.1145/3387168

      Copyright © 2019 ACM

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      Publication History

      • Published: 25 May 2020

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      Acceptance Rates

      ICVISP 2019 Paper Acceptance Rate126of277submissions,45%Overall Acceptance Rate186of424submissions,44%

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