A Generalized Approach to Optimize Subgroup Parameters

Abstract

The comparison of the two subgroup methods, the fitting method and the moment method, was made. It was proved that the both methods are identical under a special condition for the background cross section. More detailed analysis was done from the actual derivation process of the two methods and a generalized formulation was shown that is applicable to the both methods. It became clear that the moment method is regarded as a modified version of the fitting method with a flexible weighting function. It was also concluded that the two methods are identical when the parameter of the moment method takes a specified value (I¼1).Two optimization procedures were proposed to obtain the best subgroup parameters by the use of the least square fitting. One of the methods enables to reduce the error in effective cross section from 6 to 2%.