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Bayesian likelihood methods for estimating the end point of a distribution
Author(s) -
Hall Peter,
Wang Julian Z.
Publication year - 2005
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00523.x
Subject(s) - weibull distribution , estimator , mathematics , parametric statistics , likelihood function , inverse gamma distribution , marginal likelihood , statistics , bayesian probability , point estimation , generalized gamma distribution , limiting , maximum likelihood , distribution (mathematics) , inverse chi squared distribution , asymptotic distribution , gamma distribution , point (geometry) , distribution fitting , probability distribution , normal gamma distribution , mathematical analysis , engineering , geometry , mechanical engineering
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.