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New robust tests for the parameters of the Weibull distribution for complete and censored data

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  • Liesa Denecke
  • Christine Müller

Abstract

Using the likelihood depth, new consistent and robust tests for the parameters of the Weibull distribution are developed. Uncensored as well as type-I right-censored data are considered. Tests are given for the shape parameter and also the scale parameter of the Weibull distribution, where in each case the situation that the other parameter is known as well the situation that both parameter are unknown is examined. In simulation studies the behavior in finite sample size and in contaminated data is analyzed and the new method is compared to existing ones. Here it is shown that the new tests based on likelihood depth give quite good results compared to standard methods and are robust against contamination. They are also robust in right-censored data in contrast to existing methods like the method of medians. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Liesa Denecke & Christine Müller, 2014. "New robust tests for the parameters of the Weibull distribution for complete and censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 585-607, July.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:5:p:585-607
    DOI: 10.1007/s00184-013-0454-8
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    References listed on IDEAS

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    1. Denecke, Liesa & Müller, Christine H., 2011. "Robust estimators and tests for bivariate copulas based on likelihood depth," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2724-2738, September.
    2. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    3. Waltraud Kahle, 1996. "Estimation of the parameters of the Weibull distribution for censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 27-40, December.
    4. Romanazzi, Mario, 2009. "Data depth, random simplices and multivariate dispersion," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1473-1479, June.
    5. Karl Mosler, 2003. "Central Regions and Dependency," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 5-21, March.
    6. P. Wong & S. Wong, 1982. "A curtailed test for the shape parameter of the Weibull distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 29(1), pages 203-209, December.
    7. Chen, Zhenmin, 1997. "Statistical inference about the shape parameter of the Weibull distribution," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 85-90, November.
    8. Lu Lin & Minghua Chen, 2006. "Robust estimating equation based on statistical depth," Statistical Papers, Springer, vol. 47(2), pages 263-278, March.
    9. Kris Boudt & Derya Caliskan & Christophe Croux, 2011. "Robust explicit estimators of Weibull parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 187-209, March.
    10. Wellmann, Robin & Harmand, Peter & Müller, Christine H., 2009. "Distribution-free tests for polynomial regression based on simplicial depth," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 622-635, April.
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    Cited by:

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    4. Pierre‐Yves Deléamont & Elvezio Ronchetti, 2022. "Robust inference with censored survival data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1496-1533, December.

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