Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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On UMVU Estimator of Parameters in Lognormal Distribution

  • Lee, In-Suk (Department of statistics, Kyungpook National University) ;
  • Kwon, Eun-Woo (Department of statistics, Kyungpook National University)
  • Published : 1999.04.30
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Abstract

To estimate the mean and the variance of a lognormal distribution, Finney (1941) derived the uniformly minimun variance unbiased estimators(UMVUE) in the form of infinite series. However, the conditions ${\sigma}^{2}\;>\;n\;and\;{\sigma}^{2}\;<\;\frac{n}{4}$ for computing $E(\hat{\theta}_{AM})\;and\;E(\hat{\eta}^{2}_{AM})$ are necessary. In this paper, we give an alternative derivation of the UMVUE's.

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References

  1. J. Amer. Statist. Assoc. v.65 Estimation in lognormal linear models Bradu, D,;Mundlak, Y.
  2. Commun. Statist.;-Theory Meth. v.A6 no.10 Minimum variance unbiased estimators of the ratio of means of two lognormal variates and of two gamma variates Crow, E. L.
  3. J. Royal Statist. Soc. Ser.B v.7 On the distribution of a variate whose logarithm is normally distributed Finney, D. J.
  4. Distribution in statistics : Continuous Univariate Distributions Johnsan, N. L.;Kotz, S.
  5. Theory of point estimation Lehmann, E.L.
  6. The advanced theory of statistics(4th Ed.) v.2 Kendall, M.;Stuart, A.
  7. Commun. Statist.-Theory Meth. v.A10111127-1147 Uniformly minimum variance unbiased estimation in lognormal and related distribution Shimizu, K.;Iwase, K.