On expectations associated with maximum likelihood estimation in the Weibull distribution

This short paper outlines a framework for deriving the expectations associated with maximum likelihood estimation in the two parameter Weibull distribution; these expectations involve tenns appearing in the derivates of the Weibull probability density function. This framework allows known results to be presented in a unified manner. For standard likelihood considerations, interests centres on the frrst and second order derivatives; however, we also give the expectations of third derivatives, which appear in more advanced likelihood-based results.