PERCENTILE POINT ESTIMATION IN THE 3 PARAMETER WEIBULL DISTRIBUTION BY THE EXTENDED MAXIMUM-LIKELIHOOD ESTIMATE

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.