A least deviation approach for credibility estimation : an alternative approach to Buhlmann's credibility

摘要

All previously derived univariate measures of credibility are much affected byoutlier(s) and their multivariate or hierarchical or regression counterparts on the other hand, fail tocope with the observations of non-normal populations. All of them considered traditional measureof risk (that uses the squared error loss function) and variance (or, standard deviation) that fail tocapture fully the “true dispersion” of the data for estimating credibility. Moreover, maximum ofthe credibility estimators are based on normality approximations of the parent population of thedata.Attempts have been made here to find new robust measures of credibility which are based on allobservations and one dimensional dispersion measures. These measures are useable to any lossdistribution irrespective of shape of that distribution (symmetric and/or asymmetric lossdistribution) and are less affected by outlier(s) and/or extreme observation(s).