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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.

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Bibliographic Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 1203.

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Length: 9 pages
Date of creation: 12 Sep 2012
Date of revision:
Handle: RePEc:vic:vicewp:1203

Note: ISSN 1485-6441
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Postal: PO Box 1700, STN CSC, Victoria, BC, Canada, V8W 2Y2
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Web page: http://web.uvic.ca/econ
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Keywords: J-shaped distribution; maximum likelihood; method of moments; unbiased estimation; mean squared error; bathtub hazard; finite support;

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  1. Ali Genç, 2012. "Moments of order statistics of Topp–Leone distribution," Statistical Papers, Springer, Springer, vol. 53(1), pages 117-131, February.
  2. Saralees Nadarajah & Samuel Kotz, 2003. "Moments of some J-shaped distributions," Journal of Applied Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 30(3), pages 311-317.
  3. Saralees Nadarajah, 2009. "Bathtub-shaped failure rate functions," Quality & Quantity: International Journal of Methodology, Springer, Springer, vol. 43(5), pages 855-863, September.
  4. William J. Reed, 2011. "A flexible parametric survival model which allows a bathtub-shaped hazard rate function," Journal of Applied Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 38(8), pages 1665-1680, August.
  5. 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, Taylor & Francis Journals, vol. 32(7), pages 715-722.
  6. Jacob Schwartz & Ryan T. Godwin & David E. Giles, 2011. "Improved Maximum Likelihood Estimation of the Shape Parameter in the Nakagami Distribution," Econometrics Working Papers, Department of Economics, University of Victoria 1109, Department of Economics, University of Victoria.
  7. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, Elsevier, vol. 19(3), pages 169-176, February.
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