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A Note on Improved Estimation for the Topp-Leone Distribution

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Abstract

The Topp-Leone distribution is attractive for reliability studies as it has finite support and a bathtub-shaped hazard function. We compare some properties of the method of moments, maximum likelihood, and bias-adjusted maximum likelihood estimators of its shape parameter. The last of these estimators is very simple to apply and dominates the method of moments estimator in terms of relative bias and mean squared error.

Suggested Citation

  • David E. Giles, 2012. "A Note on Improved Estimation for the Topp-Leone Distribution," Econometrics Working Papers 1203, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:1203
    Note: ISSN 1485-6441
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    References listed on IDEAS

    as
    1. Jacob Schwartz & Ryan T. Godwin & David E. Giles, 2011. "Improved Maximum Likelihood Estimation of the Shape Parameter in the Nakagami Distribution," Econometrics Working Papers 1109, Department of Economics, University of Victoria.
    2. Saralees Nadarajah, 2009. "Bathtub-shaped failure rate functions," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(5), pages 855-863, September.
    3. William J. Reed, 2011. "A flexible parametric survival model which allows a bathtub-shaped hazard rate function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1665-1680, August.
    4. Jacob Schwartz & David E. Giles, 2011. "Biased-Reduced Maximum Likelihood Estimation for the Zero-Inflated Poisson Distribution," Econometrics Working Papers 1102, Department of Economics, University of Victoria.
    5. David E. Giles & Hui Feng & Ryan T. Godwin, 2016. "Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2465-2483, April.
    6. Lemonte, Artur J. & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2007. "Improved statistical inference for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4656-4681, May.
    7. Jacob Schwartz & David E. Giles, 2016. "Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 465-478, January.
    8. Ali Genç, 2012. "Moments of order statistics of Topp–Leone distribution," Statistical Papers, Springer, vol. 53(1), pages 117-131, February.
    9. M. E. Ghitany & S. Kotz & M. Xie, 2005. "On some reliability measures and their stochastic orderings for the Topp-Leone distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 715-722.
    10. J. René Van Dorp & Samuel Kotz, 2006. "Modeling Income Distributions Using Elevated Distributions On A Bounded Domain," World Scientific Book Chapters, in: Rafael Herrerías Pleguezuelo & José Callejón Céspedes & José Manuel Herrerías Velasco (ed.), Distribution Models Theory, chapter 1, pages 1-25, World Scientific Publishing Co. Pte. Ltd..
    11. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
    12. Saralees Nadarajah & Samuel Kotz, 2003. "Moments of some J-shaped distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 311-317.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    J-shaped distribution; maximum likelihood; method of moments; unbiased estimation; mean squared error; bathtub hazard; finite support;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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