S.P. Mukherjee

The family of Weibull distribution is widely used as a model of the time to failure in many engineering applications. The absence of explicit solutions to the likelihood equations for the Weibull parameters has prompted various alternative methods, including some modifications of existing methods for parameter estimation. The use of the property that expected value of T.h(T) is the shape parameter leads to an estimate based on some non-parametric estimate of h(T) the failure rate, as one non-conventional method.The author has examined the joint asymptotic efficiency of the moment estimators relative to the mle's as a function of the orders of the two moments, allowed to be positive fractions, and has found the optimal choice of these orders to yield quite a high efficiency. Another estimator suggested by the author (with S.K.Sinha) makes use of the property that log-failure rate is linearly related to log-time and finds approximations to log-failure rate in terms of Fisher's and Hotelling's methods for estimating Logistic parameters. Problems involved in this approach have been indicated.