On nonlinear weighted errors-in-variables parameter estimation problem in the three-parameter Weibull model

This paper is concerned with the three-parameter Weibull distribution which is widely used as a model in reliability and lifetime studies. In practice, the Weibull model parameters are not known in advance and must be estimated from a random sample. Difficulties in applying the method of maximum likelihood to three-parameter Weibull models have led to a variety of alternative approaches in the literature. In this paper we consider the nonlinear weighted errors-in-variables (EIV) fitting approach. As a main result, two theorems on the existence of the EIV estimate are obtained. An illustrative example is also included.