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...

Many quantities arising in non-life insurance depend on claim severity distributions, which are usually modeled assuming a parametric form. Obtaining good estimates of the quantities, therefore, reduces to having good estimates of the model parameters. However, the notion of ‘good estimate'...

Due to advances in extreme value theory, the generalized Pareto distribution (GPD) emerged as a natural family for modeling exceedances over a high threshold. Its importance in applications (e.g., insurance, finance, economics, engineering and numerous other fields) can hardly be overstated and...

In actuarial practice, regression models serve as a popular statistical tool for analyzing insurance data and tariff ratemaking. In this paper, we consider classical credibility models that can be embedded within the framework of mixed linear models. For inference about fixed effects and...

A single-parameter Pareto model, Pareto I, arises in many areas of application such as pricing of insurance risks, measuring income or wealth inequality in economics, or modeling lengths of telephone calls in telecommunications. In insurance, for example, it is common to work with data that are...

``The rich are getting richer'' implies that the population income distributions are getting more right skewed and heavily tailed. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are all...