Titelaufnahme

For independent exponentially distributed random variables Xi, i 2 N with distinct rates i we consider sums P i2A Xi for A N which follow generalized exponential mixture (GEM) distributions. We provide novel explicit results on the conditional distribution of the total sum P i2N Xi given that a subset sumP j2A Xj exceeds a certain threshold value t > 0, and vice versa. Moreover, we investigate the characteristic tail behavior of these conditional distributions for t ! 1. Finally, we illustrate how our probabilistic results can be applied in practice by providing examples from both reliability theory and risk management.