The Weighted Maximum Product of Spacings for Extreme Value Distributions

The Maximum Product of Spacing (MPS) is an alternative parameter estimation method for the Maximum Likelihood Estimator (MLE), since the MLE may not exist in some circumstances. However, the MPS estimator still has some weaknesses despite being an alternative method. This is due to the variations in distance between data points, particularly with extreme data points, as the MPS is based on the calculation of spacings in a data set. It is also possible that any slight difference in the estimation of the parameters may have a substantial impact on the fitted values of the extreme value distribution. As a consequence, it is very important to estimate the parameters of the extreme value distribution as accurately as possible. Therefore, the power of the mean function could be introduced and considered as a weight function, leading to the weighted MPS. This paper shows the improvement of the MPS method. The Weighted Maximum Product of Spacing (WMPS) is a method that gives weights to the maximization of the logarithm of the spacings in the data set. This is done to reduce the root mean square error of the models and improve the goodness of fit of the extreme value distributions.