Parameter Estimation In A Minimum-Type Model By The Least-Squares Method - A Monte Carlo Study

This paper deals with parameter estimation for a minimum-type distribution function - G(x) = 1 - exp[- x/θ₁ - θ₂ x^α]. A ²Two modifications of the least-squares method (LSM) proposed by Bain and Antle are investigated and compared by means of the Monte Carlo study. The first one is an estimation of θ₁, θ₂, a by solving the set of three equations defining the stationary point of the sum of squares. It is shown that the solution reduces to solving only one equation for the parameter a. It is demonstrated that there is a rather high probability of not obtaining a solution in the parameter space Ω = {θ₁ >0, θ₂ > 0, α>0\}. The performance of LSM can be improved considerably when only two parameters - θ₂ and α - are unknown. We investigate this using an independent method for obtaining an estimate for θ₁.