A review of some existence results on parameter estimation problem in the three-parameter Weibull model

In this paper we consider the ordinary least squares (OLS) and errors-in-variables (EIV) problems for a three-parameter Weibull model F(t;alpha,beta,eta)=[1-exp[-(1-alpha/eta)(beta))].x((alpha,infinity))(t), alpha >= 0,beta,eta>0, which is widely employed as a model in reliability and lifetime studies. We will systematize some of our results pertaining to the existence of the OLS and EIV estimate, which were proved in papers [16], [17] and [19]. An illustrative numerical example is also included.