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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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