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For the basic maximum likelihood estimating function of the two parametersWeibull distribution, a simple proof on its global monotonicity is given toensure the existence and uniqueness of its solution. The boundary of thefunction's first-order derivative is defined based on its scale-free property.With a bounded derivative, the possible range of the root of this function canbe determined. A novel root-finding algorithm employing these establishedresults is proposed accordingly, its convergence is proved analytically aswell. Compared with other typical algorithms for this problem, the efficiencyof the proposed algorithm is also demonstrated by numerical experiments.

A Bounded Derivative Method for the Maximum Likelihood Estimation on Weibull Parameters