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A matching prior based on the modified profile likelihood for the common mean in multiple log-normal distributions

Author

Listed:
  • Yongku Kim

    (Kyungpook National University)

  • Woo Dong Lee

    (Daegu Haany University)

  • Sang Gil Kang

    (Sangji University)

Abstract

In this paper, we develop a matching prior for the common mean in several log-normal distributions. For this problem, assigning priors appropriately for the common log-normal mean is challenging owing to the presence of nuisance parameters. Matching priors, which are priors that match the posterior probabilities of certain regions within their frequentist coverage probabilities, are commonly used in this problem. However, a closed form posterior under the derived first order matching prior is not available; further, the second order matching prior is difficult to be derived in this problem. Thus, alternatively, we derive a matching prior based on a modification of the profile likelihood. Simulation studies show that this proposed prior meets the target coverage probabilities very well even for small sample sizes. Finally, we present a real example.

Suggested Citation

  • Yongku Kim & Woo Dong Lee & Sang Gil Kang, 2020. "A matching prior based on the modified profile likelihood for the common mean in multiple log-normal distributions," Statistical Papers, Springer, vol. 61(2), pages 543-573, April.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0950-4
    DOI: 10.1007/s00362-017-0950-4
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    References listed on IDEAS

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    1. Gupta, Ramesh C. & Li, Xue, 2006. "Statistical inference for the common mean of two log-normal distributions and some applications in reliability," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3141-3164, July.
    2. Jianrong Wu & Guoyong Jiang & A. C. M. Wong & Xiang Sun, 2002. "Likelihood Analysis for the Ratio of Means of Two Independent Log-Normal Distributions," Biometrics, The International Biometric Society, vol. 58(2), pages 463-469, June.
    3. S. Lin, 2013. "The higher order likelihood method for the common mean of several log-normal distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 381-392, April.
    4. Li, Xinmin, 2009. "A generalized p-value approach for comparing the means of several log-normal populations," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1404-1408, June.
    5. Longford, N.T. & Pittau, M.G., 2006. "Stability of household income in European countries in the 1990s," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1364-1383, November.
    6. Dal Kim & Sang Kang & Woo Lee, 2006. "Noninformative priors for linear combinations of the normal means," Statistical Papers, Springer, vol. 47(2), pages 249-262, March.
    7. D. Kim & S. Kang & W. Lee, 2009. "Noninformative priors for the normal variance ratio," Statistical Papers, Springer, vol. 50(2), pages 393-402, March.
    8. Schaarschmidt, Frank, 2013. "Simultaneous confidence intervals for multiple comparisons among expected values of log-normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 265-275.
    9. Paramjit S. Gill, 2004. "Small-Sample Inference for the Comparison of Means of Log-Normal Distributions," Biometrics, The International Biometric Society, vol. 60(2), pages 525-527, June.
    10. Ventura, Laura & Cabras, Stefano & Racugno, Walter, 2009. "Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 768-774.
    11. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
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