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