Klüppelberg, ClaudiaSeifert, Miriam Isabel2020-02-142020-02-142020http://hdl.handle.net/2003/3857010.17877/DE290R-20489For independent exponentially distributed random variables Xi, i ∈ N with distinct rates λi we consider sums ∑i∈AXi for A⊆N which follow generalized exponential mixture (GEM) distributions. We provide novel explicit results on the conditional distribution of the total sum ∑i∈NXi giventhat a subset sum ∑j∈NXj exceeds a certain threshold value t > 0, and vice versa. Moreover, we investigate the characteristic tail behavior of these conditional distributions for t → ∞,. Finally, we illustrate how our probabilistic results can be applied in practice by providing examples from both reliability theory and risk management.enDiscussion Paper / SFB823;2/2020conditional distributiontail behaviorrisk managementreliability theoryphase-type distributionsgeneralized exponential mixture distributionexponential distributionconvolution310330620working paperBedingte WahrscheinlichkeitsverteilungExponentialverteilungZusammengesetzte Verteilung