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The higher order likelihood method for the common mean of several log-normal distributions

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  • S. Lin

Abstract

In this paper, we discuss interval estimation for the common mean of several heterogeneous log-normal (LN) populations. The proposed procedure is based on a higher order likelihood method. The merits of our proposed method are numerically compared with other three methods with respect to their expected lengths and coverage probabilities. Numerical studies have shown that the coverage probabilities of the proposed method are very accurate even for very small samples. The methods are also illustrated with an example. Copyright Springer-Verlag 2013

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  • 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.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:3:p:381-392
    DOI: 10.1007/s00184-012-0393-9
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    References listed on IDEAS

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    1. Ib M. Skovgaard, 2001. "Likelihood Asymptotics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 3-32, March.
    2. 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.
    3. 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.
    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. Wu, Jianrong & Wong, A. C. M., 2004. "Improved interval estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 809-821, November.
    6. 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.
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    Cited by:

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    2. 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.

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