In a large class of hazard models with proportional unobserved heterogeneity, the distribution of the heterogeneity among survivors converges to a gamma distribution. This convergence is often rapid. We derive this result as a general result for exponential mixtures and explore its implications...

For the studies of wealth, inequality and poverty, the analysis of income distribution of the individuals is a crucial issue. In practice, however, only aggregated data are available, either in groups or as a few quantiles of the distribution. To perform counterfactual exercises, it is desirable...

Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity...