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'...

``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...

Human longevity is changing; but at what rate? Insurance claims are increasing; but at what rate? Are the trends that we glean from data true or illusionary? The shocking fact is that true trends might be quite different from those that we actually see from visualized data. Indeed, in some...

To accommodate numerous practical scenarios, in this paper we extend statistical inference for smoothed quantile estimators from finite domains to infinite domains. We accomplish the task with the help of a newly designed truncation methodology for discrete loss distributions with infinite...

Recent reports about the condition of the Wisconsin dairy industry have not been all that good. According to the National Agricultural Statistics Service (NASS), dairy cow numbers in Wisconsin have been steadily dropping over the last few years while total milk production has, at best, held...

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples...

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...

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...