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Bayesian likelihood methods for estimating the end point of a distribution

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  • Peter Hall
  • Julian Z. Wang

Abstract

Summary. We consider maximum likelihood methods for estimating the end point of a distribution. The likelihood function is modified by a prior distribution that is imposed on the location parameter. The prior is explicit and meaningful, and has a general form that adapts itself to different settings. Results on convergence rates and limiting distributions are given. In particular, it is shown that the limiting distribution is non‐normal in non‐regular cases. Parametric bootstrap techniques are suggested for quantifying the accuracy of the estimator. We illustrate performance by applying the method to multiparameter Weibull and gamma distributions.

Suggested Citation

  • Peter Hall & Julian Z. Wang, 2005. "Bayesian likelihood methods for estimating the end point of a distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 717-729, November.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:5:p:717-729
    DOI: 10.1111/j.1467-9868.2005.00523.x
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    Cited by:

    1. HaiYing Wang & Nancy Flournoy & Eloi Kpamegan, 2014. "A new bounded log-linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 695-720, July.
    2. Castillo, Joan del & Serra, Isabel, 2015. "Likelihood inference for generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 116-128.
    3. Stéphane Girard & Armelle Guillou & Gilles Stupfler, 2012. "Estimating an endpoint with high-order moments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 697-729, December.
    4. Nagatsuka, Hideki & Kamakura, Toshinari & Balakrishnan, N., 2013. "A consistent method of estimation for the three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 210-226.
    5. Ouindllassida Jean-Etienne Ou´edraogo & Edoh Katchekpele & Simplice Dossou-Gb´et´e, 2021. "Marginalized Maximum Likelihood for Parameters Estimation of the Three Parameter Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(4), pages 1-62, July.
    6. Toru Ogura & Takatoshi Sugiyama & Nariaki Sugiura, 2020. "Estimation of the Shape Parameter of a Wear-Out Failure Period for a Three-Parameter Weibull Distribution in a Small Sample," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-39, November.
    7. Wang, HaiYing & Flournoy, Nancy, 2015. "On the consistency of the maximum likelihood estimator for the three parameter lognormal distribution," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 57-64.
    8. Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2012. "Estimating an endpoint with high order moments in the Weibull domain of attraction," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2136-2144.
    9. Wang, Haiying & Sun, Dongchu, 2012. "Objective Bayesian analysis for a truncated model," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2125-2135.

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