A modified MPS method for fitting the 3-parameter Weibull distribution

The maximum likelihood estimators for the parameters in a 3-parameter Weibull distribution sometimes do not exist. A variety of alternative approaches have been developed in the literature to solve this problem, and the maximum product of spacing (MPS) method is a good alternative. This paper shows that the MPS method can underestimate the shape parameter and the estimators of the location and scale parameters may be biased. A modified MPS method is proposed to avoid these problems. The appropriateness of the proposed approach is illustrated using two examples.