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Inference with the lognormal distribution

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  • Nicholas Longford

Abstract

Several estimators of the expectation, median and mode of the lognormal distribution are derived. They aim to be approximately unbiased, efficient, or have a minimax property in the class of estimators we introduce. The small-sample properties of these estimators are assessed by simulations and, when possible, analytically. Some of these estimators of the expectation are far more efficient than the maximum likelihood or the minimum-variance unbiased estimator, even for substantial samplesizes.

Suggested Citation

  • Nicholas Longford, 2008. "Inference with the lognormal distribution," Economics Working Papers 1104, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:1104
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    References listed on IDEAS

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    1. P. Royston, 2001. "The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(1), pages 89-104.
    2. 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.
    3. Zabel, Jeffrey E, 1999. "Controlling for Quality in House Price Indices," The Journal of Real Estate Finance and Economics, Springer, vol. 19(3), pages 223-241, November.
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    More about this item

    Keywords

    X2 distribution; efficiency; lognormal distribution; minimax estimator; Taylor expansion;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods

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