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...

For at least a century academics and governmental researchers have been developing measures that would aid them in understanding income distributions, their differences with respect to geographic regions, and changes over time periods. It is a challenging area due to a number of reasons, one of...

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios,...

The prominence of the Euler allocation rule (EAR) is rooted in the fact that it is the only return on risk-adjusted capital (RORAC) compatible capital allocation rule. When the total regulatory capital is set using the value-at-risk (VaR), the EAR becomes -- using a statistical term -- the...