Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as...

Insurance loss data are usually in the form of left-truncation and right-censoring due to deductibles and policy limits, respectively. This paper investigates the model uncertainty and selection procedure when various parametric models are constructed to accommodate such left-truncated and...

Over the last decade, researchers, practitioners, and regulators had intense debates about how to treat the data collection threshold in operational risk modeling. There are several approaches under consideration --- the empirical approach, the "naive'' approach, the shifted approach, and the...

Episode Treatment Groups (ETGs) classify related services into medically relevant and distinct units describing an episode of care. Proper model selection for those ETG based costs is essential to adequately price and manage health insurance risks. The optimal loss model (or model probabilities)...

The probabilistic behavior of the claim severity variable plays a fundamental role in calculation of deductibles, layers, loss elimination ratios, effects of inflation, and other quantities arising in insurance. Among several alternatives for modeling severity, the parametric approach continues...

Two recent papers by Dornheim and Brazauskas (2011a, b) had introduced a new likelihood-based approach for robust-efficient fitting of mixed linear models and showed that it possesses favorable large- and small-sample properties which yield more accurate premiums when extreme outcomes are...

A rich variety of probability distributions has been proposed in the actuarial literature for fitting of insurance loss data. Examples include: lognormal, log-t, various versions of Pareto, loglogistic, Weibull, gamma and its variants, and generalized beta of the second kind distributions, among...

In many areas of application mixed linear models serve as a popular tool for analyzing highly complex data sets. For inference about fixed effects and variance components, likelihood-based methods such as (restricted) maximum likelihood estimators, (RE)ML, are commonly pursued. However, it is...

We consider robust and efficient fitting of claim severity models whose parameters are estimated using the method of trimmed moments, which was recently introduced by Brazauskas, Jones, and Zitikis (2009). In this article, we take the ‘next' step by going beyond the theory and simulations, and...