H. Hirose

This paper describes the extended estimate of a percentile point obtained by the maximum likelihood method of the Weibull distribution. The extension requires that we evaluate the convergence of the Newton-Raphson iteration method by the convergence of the likelihood instead of by the convergence of the parameters. This estimate is called the "EMLE" (extended maximum likelihood estimate). This concept has two benefits; the first is that we can estimate percentile points even when we fail to find converged parameters and the second is that biases of the percentile points given by EMLE are smaller than those given by other closed-form methods. These two properties are clearly seen when the shape parameter is large. EMLE is useful when lower tail percent percentile point estimators are needed. The discussion in this paper is concerned only with complete, i.e. uncensored failure samples.

　

Times Cited in Web of Science: 7

Times Cited in Google Scholar: 16

Cited in Books:

WoS: APPLIED MATHEMATICAL MODELLING 巻: 37 号: 9 ページ: 6354-6363 DOI: 10.1016/j.apm.2013.01.027 発行: MAY 1 2013; AMERICAN STATISTICIAN 巻: 65 号: 1 ページ: 44-54 発行: FEB 2011; COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 巻: 40 号: 16 特別号: SI ページ: 2985-2996 DOI: 10.1080/03610926.2011.562785 発行: 2011; EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 177 (1): 604-611 FEB 16 2007; IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 9 (4): 524-536 AUG 2002; TECHNOMETRICS 39 (2): 199-210 MAY 1997; IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 3 (1): 43-55 FEB 1996